http://www.youtube.com/watch?v=xiNvQ-g1XGs&list=PLDBBB98ACA18EF67C&index=19
This (admittedly biased) youtuber has a pretty thorough criticism of the study. The bottom line is that cholesterol tends to drop off before death (6:26 in the video), not just because cholesterol-lowering medications are administered to those at highest risk of heart attack (as Kawoomba points out), but also because of other diseases. When you correct for this, or follow people throughout their lives, this reverse causation effect disappears, and you find exactly the association you would expect: higher cholesterol associates with higher cardiovascular and total mortality (10:21).
I think that studies like this one are like studies showing that overweight is "protective" against mortality - when the obvious alternative explanation is that smoking, cancer, and other diseases can prevent weight gain, or cause weight loss, just before they kill you! Obviously, this would mask or even reverse the association between overweight (high cholesterol) and death, even if overweight (high cholesterol) causes death.
It's a good theory and the priors for it being true are high, but the one study that should have been able to test it directly got the opposite results as the theory would have predicted; patients with consistently low cholesterol over twenty years had higher mortality rate than patients with sudden drops in cholesterol.
One study isn't enough to draw any conclusions, but it does prevent me from considering the issue completely solved despite the elegance of this explanation.
Discussion of a Norwegian study looking at 50,000 people who didn't have pre-existing heart disease for ten years. http://drmalcolmkendrick.files.wordpress.com/2012/09/mortality-and-cholesterol1.png?w=600&h=309
Here's the study.
Here's the actual conclusion from the study, which dhoe pointed out in comments is considerably milder than the quote above:
However, the chart (the png link above-- I don't know how to make the image appear) shows that the all cause mortality for women was lower if their cholesterol results were higher.
A different big study which also found that low cholesterol was dangerous, but high cholesterol was also dangerous in terms of heart attacks, though mostly for men under fifty, and (I think) not so much for women.
A comment explains that the usual test for cholesterol isn't actually for cholesterol, it's for the lipoproteins which keep all sorts of fat molecules from forming large blobs in a watery environment.
This sort of thing appeals to a number of my prejudices, so I'm hoping to get some more meticulous angles on it from LW.
Post edited to add discussion of the conclusion of the Norwegian study.