It doesn't burn off the oil, but from the way it was explained to me, it goes extremely lean and there is a short temp spike. That is what he said does the damage. There is always residual oil in it, but the temp spike from it going lean is what he said does the damage. The oil was also used as an example because you shut the flow of fuel off, you also shut the flow of oil off. It has some, but not what it requires at a full flow, also causing the heat spike. I am not an expert, and can only relate what has been said to me by people who know better and from experience.

If you are unsure, afer run oil will never hurt, but from what I have seen, running it and shutting off the fuel when you are done to clear the engine of everything in it does more damage than not. I will continue to do it the way I have for over 27 years. Go with what you feel is best. I don't know of a proven test done either way. Probably is one somewhere though.