How statins work is irrelevant - for all I care they might just as well be magical pills made from literal fairy dust. The intricate details of how this works, and how statins affect mortality is of interest only to medical researchers looking to develop new drugs.
What I do care about is the fact that when you give 100 000 people statins vs placebo then more people die in the control group.
As a result, deciding to NOT TREAT 100 000 people who are like those in the study will cause additional and completely preventable deaths. Even if the cholesterol model is completely wrong the fact still remains that fewer people die when given the drug.
In that case (99 deaths from side effects for every death prevented) the drug would never be prescribed, or be removed as soon as this information was discovered (e.g. phen-fen)
Go find me a single drug without side effects then. Obviously every drug has side effects, and this is taken into consideration when prescription recommendations are made - for example, aspirin is prescribed for high risk patients (when the benefit of preventing a heart attack outweighs the risk of a bleed) but not routinely given to everyone. Since statins are quite safe and cheap, it is reasonable enough to prescribe them widely.
Addendum:
[Consider the following a hypothetical example - I did not research cholesterol beyond the "fewer people in the treatment group died compared to the control group". You may well be correct about this specific case but this is about the principle in general]
The other thing is that you seem to have rather missed the point of science based medicine - you have a model of how cholesterol and are linked: You noticed that people with high cholesterol are more likely to die than people with normal cholesterol, and you noticed that people who are given a drug have both lower cholesterol levels and lower mortality. It is not unreasonable to think that lowering cholesterol caused the decrease in mortality, but you do not KNOW that.
As such, lowering cholesterol by other means might have the same effect (if you are correct) or no effect at all (if you are wrong about the mechanism by which the drug prevents deaths).
Keeping in mind that there is no shortage of theoretically plausible drugs which never made it to market because they flat out do not work in actual patients, a treatment that is proven to be effective sounds better than a treatment that might be effective if you guessed correctly.
If/when research demonstrating that other ways of lowering cholesterol are just as effective (or better) than the drug and/or safer then obviously NHS recommendations will change as well
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