As I understand it (disclaimer: I'm not a doctor), the inflammation results in damage to the blood vessels, which your body repairs by using cholesterol, among other things, that are in your blood. When LDL cholesterol (the "bad" kind of cholesterol) is used in this way, it calcifies over time, leading to hardening of the arteries. As someone with a high CAC score and premature calcification of my arteries, my doctors have advised me to move to a low-carb diet and combine that with statin drugs to lower my LDL cholesterol. Low carbs generally means lots of meat and lots of saturated fat, which is the opposite advice that doctors traditionally have given for patients at risk of heart disease.
Lately there have been lots of studies that show that dietary LDL cholesterol is only very loosely correlated with LDL cholesterol in your blood--primarily because the cholesterol in your blood is produced in your pancreas, not ingested/absorbed from your stomach. So I did a self experiment--go on a ketosis diet for 3 months before I started taking my statins and test to see if my LDL cholesterol changed. It didn't--it went slightly down in my case. Then I went on statins--now my LDL cholesterol is at "normal" levels.
So, basically as I understand it, low carb diets can help prevent your body damaging your arteries in the first place, such that they don't need repair. Then, the statins lower my LDL cholesterol such that when my arteries do need repair, the cholesterol that is used doesn't calcify over time. Basically I'm attempting to address my heart disease from both sides: prevent the damage in the first place, and remove calcifying LDL cholesterol from my bloodstream when arterial repair is necessary.
Note that this is all pretty cutting edge stuff, and we don't have good studies to demonstrate its effectiveness yet. If you have issues with calcification of your arteries, it is best to work with your doctor to find a program that works for you.