However, to the extent the frame rebounds, the energy isn't lost, except to the extent of energy lost as heat in the process. Thus the amount of energy lost in frame flex that could be converted to speed has to be incredibly negligable.

I do think there are some perception things going on that may make a stiff frame feel faster, and may possibly even make the rider ride faster due to a confidence or motivational affect.

Switching from my Merlinextralight, a relatively flexy frame by current standards, to a 2007 Giant TCR Advanced Team, a very stiff frame, The Giant feels like pushing on the pedals gives a more instant response, whereas the Merlin feels like it doesn't accelerate as fast initially. The positive feedback makes it feel faster, and possibly inspires you to ride it faster.

Also I've noticed in fast descents, the Giant seems to carve turns better, and feel more secure in high speed turns. I attribute this in part to the stiffer frame. (Although I'm willing to consider that it may well be in my head). My confidence in the line carved with the stiffer frame gives me the confidence to corner faster.