Through retrospective studies, the statin industry has been very successful at the game of pretending that benefits derived from high cholesterol are actually due to statins, as I have described at length in an essay on the relationship between statins and fetal damage, sepsis, cancer, and heart failure. In the case of Alzheimer's, they are playing this game in reverse: they are blaming cholesterol for a very serious problem that I believe is actually caused by statins.
The statin industry has looked long and hard for evidence that high cholesterol might be a risk factor for Alzheimer's. They examined cholesterol levels for men and women of all ages between 50 and 100, looking back 30 or more years if necesssary, to see if there was ever a correlation between high cholesterol and Alzheimer's. They found only one statistically significant relationship: men who had had high cholesterol in their 50's had an increased susceptibility to Alzheimer's much later in life .
The statin industry has jumped on this opportunity to imply that high cholesterol might cause Alzheimer's, and, indeed, they have been very fortunate in that reporters have taken the bait and are promoting the idea that, if high cholesterol many years ago is linked to Alzheimer's, then statins might protect from Alzheimer's. Fortunately, there exist lengthy web pages (Cholesterol Doesn't Cause Alzheimer's) that have documented the long list of reasons why this idea is absurd.
Men who have high cholesterol in their 50's are the poster child for statin treatment: all of the studies that have shown a benefit for statins in terms of reducing the number of minor heart attacks involved men in their 50's. 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 . As will be discussed further later, people with Alzheimer's also have reduced levels of B-HDL, as well as sharply reduced levels of fatty acids, in the cerbrospinal fluid, i.e, impoverished supply of cholesterol and fats to the myelin sheath . As we saw earlier, fatty acid supply is essential as building blocks for the sulfatide that is synthesized by oligodendrocytes to keep the myelin sheath healthy .
The obvious study that needs to be done is to bin the men who had high cholesterol in their 50's into three groups: those who never took statins, those who took smaller doses for shorter times, and those who took larger doses for longer times. Such a study would not be hard to do; in fact, I suspect something like it has already been done. But you'll never hear about it because the statin industry has buried the results.
In a very long term retrospective cohort study of members of the Permanente Medical Care Program in northern California, researchers looked at cholesterol data that were obtained between 1964 and 1973 . They studied nearly ten thousand people who had remained members of that health plan in 1994, upon the release of computerized outpatient diagnoses of dementia (both Alzheimer's and vascular dementia). The subjects were between 40 and 45 years old when the cholesterol data were collected.
The researchers found a barely statistically significant result that people who were diagnosed with Alzheimer's had higher cholesterol in their 50's than the control group. The mean value for the Alzheimer's patients was 228.5, as against 224.1 for the controls.
The question that everybody ought to be asking is: for the Alzheimer's group, how did the people who later took statins stack up against the people who didn't? In extreme understatement, the authors offhandedly remark in the middle of a paragraph: "Information on lipid-lowering treatments, which have been suggested to decrease dementia risk , was not available for this study." You can be sure that, if there was any inkling that the statins might have helped, these researchers would have been allowed access to those data.
The article they refer to for support, reference  in  (which is reference  here) was very weak. The abstract for that article is repeated in full here in the Appendix. But the concluding sentence sums it up well: "A more than a modest role for statins in preventing AD [Alzheimer's Disease] seems unlikely." This is the best they can come up with to defend the position that statins might protect from Alzheimer's.
An intuitive explanation for why high cholesterol at an early age might be correlated with Alzheimer's risk has to do with apoE-4. People with that allele are known to have high cholesterol early in life , and I believe this is a protective strategy on the part of the body. The apoE-4 allele is likely defective in the task of importing cholesterol into the astrocytes, and therefore an increase in the bioavailability of cholesterol in blood serum would help to offset this deficit. Taking a statin would be the last thing a person in that situation would want to do.