[Otto]

If you severely clip a signal, and it becomes a square wave, the square wave will have high frequency components (Fourier analysis) that are perhaps not representative of the original signal. If there becomes too much high frequency content, the tweeter may receive more power than it can handle.

I haven't done all the math out (and I surely won't), but I know that the above can happen. I've blown speakers by massively underpowering them, and then trying to play them loudly (when I was a kid).

Indeed, Geoff, in this case, you are overpowering the tweeter, but it comes from underpowering the system.