Here is the basis for the widely-stated comment that low power amps can blow speakers.
Music is mostly complex sine waves. When an amp is overdriven, it starts clipping. Clipping flattens the tops of the signal, increasingly turning them into square waves. If you look at a full square wave, it goes from all the way "on" at the negative end of the cycle to all the way "on" during the positive phase with no "off" period. Also, square waves contain a lot more high frequency info. A 1 KHZ pure sine wave wave contains only 1 KHz info. A 1 KHz square wave contains a ton of higher frequency harmonics.
So, it is very easy for a clipping amplifier to send lots of power to a tweeter even though the music being played doesn't have a lot of high frequency content. This, combined with the increased "on" periods makes it easy to overheat tweeters in particular, but the other drivers can also be affected.
As others have said, though, clipped music sounds nasty and is clearly obvious to almost any listener. If this happens with your system on a regular basis, you either chose the wrong speakers or the wrong amp.