Bile is used to process food in the gut. It does not go back into our system. Bile is still produced by liver even in long fasts.
Oatmeals is a kind of elimination diet, much like carnivore diet or rice diet. The later one also lowered cholesterol.
What oatmeal diet really does is it completely eliminates essential fatty acids in food. These fatty acids are critical in VLDL production and, thusly, oatmeal diet reduces LDL levels through less production of VLDL.