Great question!
I love these fish (and more importantly, so does my wife

), and typically keep reef tanks (not FOWLR)... always wanting to take the risk.
Most people I've talked to or seen tanks with these fish have relatively large tanks with mainly SPS, and get them as juveniles... and they seem to behave pretty well. I think the danger is when they get older and more territorial (causing havoc on tankmates).
But to answer your question, I don't think corals are one of the things in their diet, but rather their aggression and/or tendency to move LR around is what causes many people to avoid putting them in their reef-tanks.