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According to this textbook, high ( >2mg/ml of blood) EDTA concentration causes swelling of platelets which lead to their fragmentation.
I know that high concentration of EDTA increases plasma osmolarity which leads to cell shrinkage , as is the case in all other blood cells, but why does it have opposite effect on platelets? Why osmotic effects aren't seen in platelets?
As it's reported in an old 1968-article by J. G. White:
Chelation of membrane calcium by EDTA appears to cause marked irregularities in the platelet wall and massive swelling of the canalicular system. Swelling of internal channals is the dominant alteration in EDTA platelets, and this change appears ultimately to be related to the breakdown of platelet granules.
Many articles followed the one reported above, but it seems that the main cause of platelets swelling in presence of EDTA is the reduction of calcium levels that causes a sort of platelet activation.
This acivation could also be linked to direct EDTA action as reported in this article by Golański et al.:
The influence of EDTA on platelet membrane dynamics closely mimicked the alterations induced upon the interaction of fibrinogen with platelet GPIIb-IIIa. Thus, the EDTAK2-induced platelet activation might result from an interference with platelet membrane protein structure and conformation and possibly relate to an “unspecific” trigerring of a signal transduction pathway.
Anyway in normal conditions the laboratory platelet volume quantification using EDTA tubes seems not to be affected if executed in 1 hour since the collection (as reported in this article by Dastjerdi et al.).
I think your question is relying on two completely different definitions of "high" EDTA. Really, both concentrations are "high" but one of them is "really really high."
The only references (for example, here or here) I can see that say anything about osmotic effects of EDTA is in the context of blood sample collection, and specifically when too small a volume is drawn into a larger tube, for example 0.5mL blood in a 5mL tube. In this circumstance, a ~liquid (blood) is added to solid EDTA powder sitting in the tube. This is already a high concentration of EDTA, it's enough to mop up all of the calcium around to prevent coagulation.
However, if you only fill the tube 10% full, there is 10X more EDTA powder pre volume than necessary to prevent clotting. This isn't just high, it's incredibly high. EDTA is usually as a potassium salt in this context, so that could be as much as ~100mOsm which would definitely cause osmotic effects, but that's on the order of a 10-fold higher concentration than your reference for platelets (which I can't access unfortunately). When you state in your question:
I know that high concentration of EDTA increases plasma osmolarity which leads to cell shrinkage
...this seems to be the best explanation, unless you can show another reference that demonstrates substantial cell shrinkage at lower (~2mg/ml) concentrations. I'm not saying there can't be some osmotic effect at that level, just that it would only be a couple percent of cell volume and would not be noticeable on anything but the finest assays.
Then on the other side of the equation, the effects on platelets are not to do with osmotic effects but rather due to a somewhat paradoxical activation of platelets, as in @DavideN's answer. Think of platelets as cells that are "primed" to expand when needed to stop a bleed; in some circumstances, it seems like EDTA can be a trigger for this process to occur, though not in others (again, see @DavideN's conflicting references).
References:
Goossens, W., DUPPEN, V., & Verwilghen, R. L. (1991). K2‐or K3‐EDTA: the anticoagulant of choice in routine haematology?. International Journal of Laboratory Hematology, 13(3), 291-295.
