Tom Naughton pointed this out
There is a clear reason why statins would promote Alzheimer’s. They cripple the liver’s ability to synthesize cholesterol, and as a consequence the level of LDL in the blood plummets. Cholesterol plays a crucial role in the brain, both in terms of enabling signal transport across the synapse and in terms of encouraging the growth of neurons through healthy development of the myelin sheath. Nonetheless, the statin industry proudly boasts that statins are effective at interfering with cholesterol production in the brain as well as in the liver.
Researchers are only recently discovering that both fat and cholesterol are severely deficient in the Alzheimer’s brain. It turns out that fat and cholesterol are both vital nutrients in the brain. The brain contains only 2% of the body’s mass, but 25% of the total cholesterol. Cholesterol is essential both in transmitting nerve signals and in fighting off infections.
High cholesterol is positively correlated with longevity in people over 85 years old, and has been shown to be associated with better memory function and reduced dementia. The converse is also true: a correlation between falling cholesterol levels and Alzheimer’s.
The original article - The Clue to Why Low Fat Diet and Statins may Cause Alzheimer's - is definitely worth reading