Nick, you put it so simply and elegantly.
I'm always amused when pilots talk about how a blade flaps as it goes round and round the mast. I suppose that in a rotor system without cyclic control, the advancing blade would surely flap upward.
But in a real helicopter, the advancing blade will not flap up- otherwise how could forward flight be maintained? Obviously, the flapping that the books talk about *must* be in equilibrium. That is, the advancing blade "flaps" up exactly the same amount as the retreating blade "flaps" down: none. Why? Primarily because the pilot is pushing forward on the stick, making the pitch of the advancing blade lower and the retreating blade higher.
Thanks to Nick for putting it in a way that makes it so clear.