I was previously taught that cholesterol affects the fluidity of a plasma membrane. At high temperatures, cholesterol decreases fluidity and at low temperatures cholesterol increases fluidity. The Khan academy and Wikipedia pages below say the same thing.
Yet, in a current college course, the textbook ("Molecular Biology of the Cell 6th" by Bruce Alberts et al.) says that cholesterol reduces the mobility of the first few CH2 groups of a phospholipid's two fatty acid chains. In this way, the cholesterol makes the lipid bilayer more rigid and decreases the lipid bilayer's permeability to small, water-soluble molecules. However, it says that cholestrol does not actually make the membrane less fluid.
Is the textbook from my current course just a more nuanced explanation, or have I misunderstood something else?