Lowering cholesterol doesn't actually reduce the risk of CAD or heart attack. Many trials have shown the same results. Statins do, however, lower heart disease risk - at least in some cohorts. This is probably why your doctor wants you to take statins and not fibrates. Fibrates are associated with increased cancer risk and all cause mortality, and they have a bigger effect on triglycerides than they do on LDL's anyways - but at comparable levels of LDL reduction to statins, they show no decrease in heart disease incidence.
The problem goes all the way back to the origin of the cholesterol theory of heart disease. The observation was (correctly) made that elevated cholesterol levels were correlated with increased risks of heart disease. However, the scientists studying it made the worst of all statistical sins and assumed correlation was causation - i.e. that the cholesterol was a cause of the heart disease, rather than a bystander. Later studies have all shown that lowering cholesterol doesn't lower heart disease risk at all.
That doesn't mean that statins don't lower heart disease risk though - and this is why they are front line drugs. They inhibit an enzyme in the liver called HMG-CoA reductase. In doing so, they down-regulate the synthesis of cholesterol. They also downregulate the production of CoQ10 (which you should be taking a lot of if you take statins). Neither of these mechanisms explain the anti-inflammatory effects of statins though. That is because they block inflammation by inhibiting isoprenoid synthesis. This, while not lowering cholesterol directly, does lower inflammation, and is probably the only useful thing that statins do. It is also why they have shown benefits in heart disease prevention.
Cholesterol is just a marker for the underlying inflammation in your body. What comes next is my view, and not necessarily scientific consensus. Cholesterol is upregulated in response to inflammation, in particular membrane peroxidation. This is because the primary, and critical role of cholesterol in the body is to increase the fluidity and integrity of cell membranes. It is interspersed between the phospholipids of the phospholipid bilayer of the cell membrane of all human cells (and all animal cells) and we cannot live without it. It is also a precursor for steroid hormone synthesis and Vitamin D3. Fungi use something called ergosterols, which are similar in function but structurally distinct, and many antifungals target the ergosterols in their cell membranes. If you buy vitamin D3, it's usually from lanolin (from sheep), and is called cholecalciferol. If you buy vitamin D2, it's from fungus - this is cheaper - and it's called ergocalciferol. The difference is whether the precursor is the animal-produced substance cholesterol or the fungus-produced substance ergosterol.
In ME, there is already evidence of increased inflammation and lipid peroxidation as well as abnormal Fenton chemistry and redox state control. The primary source in eukaryotes of oxidative stress is the mitochondrion. The electrons produced in aerobic respiration in the mitochondrial electron transport chain produce energy via oxidative phosphorylation. This is when they pass through the membrane and in the process combine an ADP with a Pi (inorganic phosphate) to make ATP.
My suspicion is that in ME, during periods of relapse, our cholesterol will go up. This may not be genetic - but people with a genetic propensity for high cholesterol will be represented in the ME population (as far as I know) at least as much as in the general population. My own cholesterol does increase during periods of relapse, and improves during times when I feel better, due to reduction in inflammation.
I am not currently on any statins. I think there may be a role for niacin, but it's not a simple question. Trials (notably the AIM-HIGH trial) have shown that while niacin does lower cholesterol further beyond statins alone, it had no effect on cardiovascular mortality. I think niacin may have more utility in lowering lp(a), a genetically determined risk factor, and there may be benefits from its ability to increase LDL particle size, but it's not clear if that's true. I have a number of genetic markers that are protective from heart disease, and both parents are completely free of it in their mid-late 60's and don't even have mild hypertension, AND I had an Agatston calcium score of 0 a few yrs ago. Additionally, I learned recently that I have a rare mutation in the APOC3 gene that cuts triglycerides in half and has similar effects on the rates of heart disease and stroke (an allele frequency of 1 in 720 in caucasians, and not found in other races) - which explained why my Italian great aunt ate 2-3 sticks of butter daily (whole, with nothing, like a banana) and lived to 90 w/o any heart disease. Thus, I wouldn't encourage everyone to follow my approach. It's based on a careful analysis of genetic and family information and tailored to me - my endocrinologist and I have discussed it at length.
Statins are tricky - we do know that overall, they lower risk of heart disease, probably in spite of lowering cholesterol. Most convincing trials have been performed for 2ndary prevention in men who have already had a heart attack.
Lots of info is available in the literature, but if you want a good history of how cholesterol got so demonized, check out Dr. Stephen Sinatra's "The Great Cholesterol Myth." My doctor recommended to me that I read it. He explains various approaches to cholesterol management. I think he also has a website where you can read stuff for free.
First though, I'd recommend you get some genetic profiling done for heart disease risk. You can do this through 23andme or similar companies or through a regular Quest or other lab with your doctor's prescription (google Berkeley Heart Test). Have a carotid doppler, and if you want even more info and have higher risk, an Agatston score.
High cholesterol IS an indication of cardiovascular risk - primarily due to excess inflammation. Lowering cholesterol, in and of itself, probably has no impact on cardiovascular risk, and it may even make things worse if the increased cholesterol is being used to fix membranes throughout the body and deal with oxidative stress. Fish oils DO lower risk of heart disease. Baby aspirin does as well, but not in everyone, and we can now determine whether or not you will benefit based on your genetics (either 23andme or quest, again - it's also part of the full berkeley heart test). Look at particle size as well - large, buoyant LDL's are FAR less dangerous (and may be protective) whereas small, dense LDL's are bad. Lipoprotein(a) or lp(a) is a major risk factor, especially if badly elevated - this is treatable to a degree with niacin, although it's not clear if this lower risk.
Any drugs that reduce cholesterol will have a risk of liver damage and rhabdomyolysis. It's a fundamental effect of lowering cholesterol. You can't get around it. Aggressively lowering cholesterol will increase rates of side effects.
Homocysteine, unlike cholesterol, is likely a modifiable risk factor. i.e. We believe, but do not know for certain, that lowering elevated homocysteine will lower heart disease risk. This, imo, is the most useful thing to do with methylation cycle genetics.
My cholesterol is not too bad right now - about 215 total, with HDL's of about 75 and triglycerides very low (can be as low as 20-30, or up to the 60's - but that's genetics, and not something most people will find). My lp(a) is borderline, so I take niacin for it. I don't think it's unreasonable or dangerous to do so, but it has risks all the same, and I get my liver function checked. Mine is by prescription, so there is less flushing (don't buy otc no-flush, it doesn't work). I take 4g of flaxseed oil and 4 fisol per day (these are enteric coated fish oils, so no regurg). I also take CoQ10. This seems to work for me, but again, I have favorable genetics here, so I can afford a less aggressive approach. In a higher risk patient, I think statins need to be considered. Get as much info as you possibly can before jumping in. Look at measures of inflammation - definitely get a hsCRP - this is well known to most docs and used pretty often - and obviously a homocysteine level as mentioned above. Sed rate can be useful but in ME tends to run really low in most and may falsely suggest lack of inflammation.
These are complex questions and should be discussed with your doctor. I have a pretty good understanding, and I still discuss it with my endo, who is very expert in this area. Statins aren't all that most docs and pharma companies would have you believe, BUT they remain the single most proven drug for cardiovascular risk prevention, especially 2ndary prevention, and especially in men. Whether the new aggressive targets are merited is controversial.
Lowering your cholesterol to "normal" range with statins does NOT have the same effect as lowering it with lifestyle changes. I know we are all limited in exercise capacity. However, we can still eat a healthy diet. Cut the trans fats from your diet completely - and don't trust the trans fat category on the label, read the ingredients for anything that says "partially hydrogenated." Sat fats are probably ok in moderation. Avoid vegetable oils (polyunsaturated) like the cheapo mazolas and similar. Cook with olive oil and peanut oil, the latter if you are going to get it very hot (olive oil at moderately high temps can convert to less healthy forms of fat - peanut oil is highly temperature resistant). These are oils that are high in monounsaturated fats, which reduce inflammation, as they divert metabolism from the arachidonic acid pathway which leads to increased synthesis of prostaglandins. Be aware that aspirin and fish oils are blood thinners - and too much can be a bad thing, especially if you have a bleeding diathesis to begin with, which may be present in ME in some people.
As I said - a very complicated question, but fortunately, one we know a great deal about. Fortunes have been poured into studying this, as it is the leading killer in the western world, so unlike treating ME, we aren't flying blind. We probably do have elevated heart disease risk from having ME though, due to excess inflammation and other factors - but likely can still take advantage of known risk markers and treatments.