"Why does eating saturated fat increase blood cholesterol?"
From your explanatory text I understand: ... as it is transported by chylomicrones and not by LDL which is commonly known as "bad" cholesterol.
I'm paraphrasing even more: How could eating saturated fat which is not transported by LDL (termed "bad cholesterol"), and for this reason should not lead to more LDL in the blood, be held responsible for "bad cholesterol"?
There are two common misunderstandings I think your question brings up (educating, to me):
Chylomicrones are not the only transporters of (saturated) fatty acids. There are the VLDL as well doing that job. The difference is termed "dietary fat" versus "endogenous fat". The liver is the body's biggest producer of (saturated) fatty acids (interestingly, the liver produces but saturated fatty acids!). This fat is transported from the liver to tissues by VLDL (Very Low Density Lipoproteins). It is no trivial knowledge that LDL is not produced by the liver "as is", only the VLDL are. However, VLDL become "bad" LDL in the bloodstream.
Lipoproteins and Chylomicrones per se, as transporter molecules, incorporate cholesterol, in different amounts and percentages of total weight. From textbooks it may be easy to tell whether cholesterol is a "part" of the transporter or being transported as "package". Cp.Dr. Malcom Mkendrick (paragraph"re-cap")
What might appear as some "breaking news" AD Cooper · 1997 "Chylomicrons are formed in the intestine and transport dietary triglyceride to peripheral tissues and cholesterol to the liver." Still another one: Enterocytes not only produce chylomicrones but VLDL, too.
Both Chylomicrones/chylomicrones-remnants and VLDL/"VLDL"(called LDL) resemble each other in their "later life" termed "remnant". What remains of VLDL after unloading fatty acid is termed LDL, and packed cholesterol may look like a building block of the lipoprotein (as the LDL receptor of tissue cell takes up LDL as is - no unloading). Hint: my misunderstanding taken for typical learner's was to think of LDL being sent off by the liver - not correct: it's VLDL off from the liver, and "remnancy" after unloading fatty acid at the veins' walls. So VLDL become LDL in the blood stream. There is a special page in Wikipedia not easy to find:Remnant cholesterol
These preliminary remarks are practical hints, as you may search for "why does eating saturated fat increase VLDL (very low density lipoproteins) and get some clues and discussion via google -instead of searching for "saturated fat and LDL
Why is LDL held responsible for "bad cholesterol"? Among the lipoproteins it has the highest load of cholesterol; and as a "remnant" transporter of cholesterol it does seem to unload cholesterol at arterial walls just as that same transporter (named VLDL at that point)= does with fatty acids - if tissue cells not in need of cholesterol do not express the LDL receptor (Nobel prize winners Brown and Goldstein's research on familial hypercholesteraemia).
That said, why then should reduction of dietary saturated food reduce VLDL and/or LDL (your question translated to that formula) as the only "clear" effect of saturated food is a higher production of chylomicrones which are very low in cholesterol?
Did you read my latest news up above? I think it is no common knowledge that chylomicrons are involved in cholesterol transport from the intestine to the liver. Simple inference from that: more cholesterol input (combined to saturated fat) causes more cholesterol output (combined to fat, VLDL which becomes LDL "on deliverance").
However, searching through literature, your question turns out to be valid - nothing is "clear" and undebated, and that goes for the following simple reasoning as well, recurring to basic knowledge (before I knew about chylomicrones delivering cholesterol to liver):
Effect of dietary saturated fat is that the liver will be able to synthetize and deliver to tissue cells more of so called endogenous fat as it receives more of fatty acids FROM tissues the more those tissues receive fatty adics from chylomicrones (see below about pathway from tissue TO Liver-Hint: it is not irrelevant in respect of your question that short fatty acids do not need chylomicrones for uptake from intestine, and it seems that in early scientific discussion the high amount of any kind of fat, saturated or not, was subject of debate).
Any surplus of fat the liver produces is transported to tissues (Stryer/Berg, Biochemistry) by
VLDL, the Very Low Density Lipoproteins.
The important crossroad of those pathways is at the arterial wall where VLDL unload endogenous fat from and made by the liver. VLDLs thus become "ILDL - Intermediate-Density Lipoproteins", half of which is returned to the liver for turnover, half of which, however, become LDL (how? By "unloading more fatty acids", cp. Berg/Stryer, Biochemistry).
So, this presumed mechanism is in favour of the quote cited: more saturated fat deliverd by chylomicrones will lead to more saturated fat in VLDL which, after unloading fatty acids, become "bad" LDL transporting cholesterol (only). More saturated fat input is seen here as a "commodity" the liver replenishes its production of endogenous fat with.
Let me give you some quote describing the pathways, to see how the liver receives (saturated) fatty acids taken in by chylomicrones that have delivered to storage fat tissues (not to liver!). VLDL are only needed for transportation FROM the liver, not to the liver. How might liver input of fatty acids, leading to bad LDL, be heightened by chylomicrone input?
[K.R. Feingold, Introduction to Lipids and Lipoproteins]
"...The exogenous lipoprotein pathway starts with the incorporation of dietary lipids into chylomicrons in the intestine. In the circulation, the triglycerides carried in chylomicrons are metabolized in muscle and adipose tissue by lipoprotein lipase releasing free fatty acids, which are subsequently metabolized by muscle and adipose tissue, and chylomicron remnants are formed (...) then taken up by the liver. The endogenous lipoprotein pathway begins in the liver with the formation of VLDL."
In Berg/Stryer,10ed., Fig. 26.16 depicts Fig 36.1 of Goodman/Gilman: The liver receives free fatty acids released into the blood by "adipose tissue", i.e. tissue cells that have received saturated fats from chylomicrones.
So, if (saturated) fat input is transported to STORAGE tissue by chylomicrones high input of fat may lead to excess, surplus storage of fat in adipose tissue, then to free fatty acids input of the liver which metabolizes to endogenous triglycerides(!) "re"-transported to storage and/or catabolic tissue. It may be a question of debate whether LDL from VLDL being turned to ILDL is a metabolic switch the aim of which is to "store as much as possible" - where, at the end of the line fat broken down in liver and re-metabolized to cholesterol by the liver (via acetyl-CoA) can be stored as cholesterol by any cell that is able to store away cholesterol,then not using cholesterol as building block of its membrane.
This point alludes to the second part of my answer that differentiates between animal and plant tissue: animal cells much more than plant cells might be able to STORE cholesterol which might explain why animal fatty tissue contains roughly 100 times more cholesterol thatn plant fatty tissue, see down below.
"The triglycerides carried in VLDL (annot. see quote above: triglycerides made by the liver) are metabolized in muscle and adipose tissue by lipoprotein lipase releasing free fatty acids and IDL are formed. The IDL are further metabolized to LDL, which are taken up by the LDL receptor in numerous tissues including the liver, the predominant site of uptake."
Surpringly, the liver emits LDL, but does have LDL-receptor.
These LDL-receptor of the liver are said to take receive "chylomicron remnant", see, for instance, Dr. Malcom Kendrick
Assuming those LDL-receptor of the liver also take up LDL that has been refused by tissue cells however, seems coherent to some basic principle of "store ("can"..) as much as you can": fat non used or stored in tissue being receivevd by the liver (free short fatty acids in blood!), liver handing its surplus back to tissue on VLDL; surplus fatty acid in liver metabolized to cholesterol, delivered to cells, cholesterol not taken up by cells returned to the liver.
Thus, deposition of bad cholesterol in veins can be seen as some last resort of storage activity, in case the liver does restrict LDL-receptors as presumably tissue cells have done before.
Thus, excess (saturated, but, as you suggest: same should apply to unsaturated) fat in food might lead to excess storage activity by bad LDL.
Refering to the distinction between saturated and unsaturated fat your question seems to focus on see, for instance, Palm Oil Consumption Increases LDL Cholesterol Compared with Vegetable Oils Low in Saturated Fat in a Meta-Analysis of Clinical Trials
Ye Sun et al., This digest of empirical studies speaks in favour of saturated fat in contrast to unsaturated fat increasing "bad" (LDL) blood cholesterol. Doing quick research I did not find any explanatory theory. Here is hint: Among unsaturated fatty acids there are some that are "essential" (as vitamins are). That is mentioned here: [bmj.com] 5https://www.bmj.com/content/361/bmj.k2139 Maybe metabolism of essential unsaturated fatty acid signals a situation where there seems to be less need to turn fatty acids into cholesterol and send it to tissue cells (because those are signalled to be able to synthesize enough on their own). That's one idea.
Even if there is somehow "clear" causality in
dietary fat - chylomicrones - liver production of endogenous fat - VLDL - VLDL remnants - LDL
it seems to be debated on if there is a difference between saturated and unsaturated fat in that respect. "You're right."
In the following, I would like to show that the statement "less fat, less cholesterol" your question refers to might still be correct, in its statement of a rule of thumb, in its empirical result, especially in what regards differentiating unsaturated and saturated fat.
Content of cholesterol in food may be considered as proportional to content of saturated fatty acids.
If you exclude saturated fatty acids from your diet according to the rule quoted in question you end up with zero input of cholesterol, and you end up as a vegetarian.
This is because
food from plants does not contain saturated fats - with a few exceptions: coconut and palmoil, nuts..., and
food from plants does not contain cholesterol in form and relevant quantity as animal food does.
"While cholesterol averages perhaps 50mg/kg total lipid in plants, it can be as high as 5 g/ kg(or more) in animal."
This is a factor of 100!
Quote is from a paper advocating the opposite point of view (no bias):
Journal of Chemical Education J. Behrman* and V. Gopalan, Cholesterol in plants
"There is a widespread belief among the public and even among chemists that plants do not contain cholesterol. This error is the result (in part) of the fact that plants generally contain only small quantities of cholesterol and that analytical methods for the detection of cholesterol in this range were not well developed until recently (1). Another reason has todo with the legalities of food labeling that allow small quan-tities of cholesterol in foods to be called zero (...). The fact is that cholesterol is widespread in the plant kingdom although other related sterols, such as β-sitosterol (henceforth referred to as sitosterol), generally occur in larger quantities. No current biochemistry text that we have examined provides an accurate account of cholesterol in plants. Here is a suggested paragraph for the next generation of biochemistry texts: More than 250 steroids have been described in plants (3).Of these, perhaps sitosterol, which differs ..."
I think it's legitimate to inversely defere from this quote that food derived from plants, at least, does not contain cholesterol in amounts relevant to nutrition.
See also Athel Cornish-Bowden
"Plants make cholesterol in very small amounts.[...] In larger quantities they produce phytosterols, chemically similar substances which can compete with cholesterol for reabsorption in the intestinal tract, thus potentially reducing cholesterol reabsorption." Wikipedia, Cholsterol
From Biology online
"Because of cholesterol that provides cell membrane structural integrity and fluidity, animal cells need not to have cell walls such as that in bacterial and plant cells."
Refering to point 2 of reasoning above:
"Most animal fats are saturated. The fats of plants and fish are generally unsaturated."
Wikipedia, Unsaturated Fat
Thus, avoiding saturated fat means avoiding animal fat, thus avoiding cholesterol.
Again, this reasoning is not what the quote cited in your question seems to refer to or be based on. As an empirical rule it might be correct for the reasons stated.
To sum up: Even if it must be admitted that there are relevant amounts of saturated fat in plants, reducing saturated fat in diet in any case reduces cholesterol input (even if that'd mean the exclusion of coconut, palm oil and peanuts, from the diet - in that way you'd sure still end up a veggie).