I respect the hard-liners' definition of 'no amplification,' but I think a better working definition is that acoustic music employs instruments (voice included) that produce their sound by primarily acoustical means, and if amplification is used to reinforce the volume it is used in such a way as to be as faithful as possible to the natural sound. Of course this is strictly speaking impossible, but you know an honest attempt at it when you hear it.
I am ambivalent about built-in pickups in acoustic guitars. I am sure that if one spent enough money one could get a faithful acoustic sound, but most of the piezo ones IMHO sound ghastly. The way a pickup frees you from being tied to a six-inch circle of space on the stage is an advantage, though.
To me the amplification/no amplification divide is not so much about the sound, but about the intimacy with the listeners that is enforced by the limitations of the instruments au-naturel. Related but different.
-Glenn