I'm curious for the technical/scientific answer to this as well. I've heard this phrase as well, but I wonder what the actual timeline looks like.
In my (very limited) experience, the longer you leave your beer on the yeast, the more it absorbs the yeast flavor.
IMPORTANT EDIT: i just reviewed my notes and remembered that i re-used yeast in these cases where i had yeastiness, by simply re-pitching on old yeast cake -> my bad, this would seem to explain the extreme yeast flavor i've had on these beers. (over-pitching).
i would still be interested to see what is the optimum time for certain strains to sit on the yeast, if in fact that is the case.
is it not true, though, that the quicker you move the beer off the cake, the cleaner the finish?