I think the reason why doctors don't warn you about low cholesterol is because (AFAIK
) in a healthy human being, your liver makes all the cholesterol you should need.
A few studies showing a correlation between low cholesterol and depression does not prove that you should eat foods high in cholesterol to be unhappy, or that a low cholesterol diet causes depression.
Several possibilities exist: Depression causes low cholesterol. Low cholesterol causes depression. Some unknown agent causes both low cholesterol and depression. Or these studies involved a statistical fluke that linked low cholesterol and depression even though no link exists. (Don't laugh -- it has been known to happen!)
Furthermore, there is question if a low cholesterol diet can cause the same effects, or if its only valid for naturally occuring low cholesterol levels regardless of diet.
So what do these studies prove? That low cholesterol may be useful as a screening agent for depression.
Contrast the possibility that low cholesterol diets cause depression with the evidence that low cholesterol levels lead to less heart disease and strokes. A rational doctor is going to advise you that lower cholesterol levels are better for you.
Hope that helps explain your doctor's reasoning.
(Btw, aren't you screened for depression whenever you have a checkup? The last checkup I had, I had questions screening me both for depression and for domestic abuse. First time I've been asked the later, but I approve of gender-neutral abuse screening!)