Could low cholesterol lead to dementia?

http://www.thecholesteroltruth.com/could-low-cholesterol-cause-dementia

In short, there’s quite a pile of evidence that strongly suggests that cholesterol is critical to proper brain functioning. In light on this, one might consider what effect cholesterol reduction may have in the long term. The review authors point out that “dietary avoidance of fats and cholesterol along with over-zealous prescription of cholesterol-reducing medications over the same decades in which there has been a parallel rise in AD [Alzheimer’s disease] prevalence.”