There is a fairly incontrovertible link in that people with familial hypercholesterolemia, a single gene mutation affecting cholesterol metabolism, have a markedly increased risk of coronary artery disease. Homozygous individuals (who are very rare) will typically suffer heart attacks in childhood if not diagnosed.

What is not as clear is whether there is a benefit of reducing cholesterol levels regardless of how that reduction is achieved. The evidence that statins, for example, lower the risk of recurrent heart attacks and strokes, for example, is beyond dispute. It is also known that these medicines lower cholesterol levels.

What has not been incontrovertibly proven, as far as I know, is that it is the lowering of cholesterol itself that is responsible for the protective effect of statins (as opposed to an effect on plaque stabilization, for example).

The evidence that other medications that lower cholesterol levels (Zetia, fibrates, niacin, etc.) also reduce the risk of vascular events is much weaker.

Now, my opinion is that it is very unlikely that cholesterol levels don't matter at all, particularly in extreme cases (for example, total cholesterol levels of 400+). Whether they matter much in more typical physiologic ranges is more of an open question.