The way that it was explained to me, years ago, that actually made sense, was that, when listening at normal levels, there can be split seconds where the needed power will peak, say, a woodblock or a gunshot, or a cymbal, or a rim shot or whip, ect. The large amp will more accuratly reproduce that sound, whereas the lesser powered amp would "clip", the wave signal would not be reproduced correctly.
Then there are companies like NAD and OUTLAW, that have very conservatively rated amp's on their receivers, but give clean sound, because they can reproduce the sounds at normal levels without clipping.
Someone else might be able to explain this in a clearer format!