What you really mean is that flaps, for a given airspeed, will produce a lower AoA, which will reduce P-factor. Yes, this is true, and is a possible mechanism too. I don't have a feel for the magnitude of the difference, though and I haven't seen any experimental data. I suspect that those who claim this is THE mechanism haven't seen any data either.
As for the drag behind the CG, it 1) doesn't matter whether or not the drag item is located behind the CG, all that matters is that the drag vector passes behind the CG, and 2) even that doesn't matter unless you can explain why there is differential drag of the flaps on the working vs failed engine.
Without real test data on a variety of airplanes of differing configurations, I think that it's intellectually dishonest to tell a student definitively why this effect occurs or even if it occurs across all multiengine airplanes. And MEI instructor gouge that's been passed around from instructor to instructor doesn't count as a source of authoritative or reliable information. The fact that an instructor can pass an oral means nothing about the accuracy of their information.