Thanks, Wikipedia can be a great source of info and I'm actually one of their donors myself. Specifically referring to '
https://en.wikipedia.org/wiki/Clipping_(audio)' which seems to be the source of your quotation:
I do recommend you carefully re-read that page which does describe the issue well, but a conclusion that the destruction of woofers is because of amps delivering more power than they are designed for is, I think, a misreading of the article.
It is true that turning up the gain of an amplifier so that you are asking it to deliver more volts than it can provide does result in the signal being clipped at the maximum output voltage of your amplifier. It is also true that the area under the signal graph is greater for the clipped signal than an unclipped sine wave signal from the same amplifier and hence more energy will be going into the speaker however the clipping isn't the cause of this it is because we have turned up the gain to produce a greater signal. If we swapped our amplifier for a more powerful higher voltage capable amplifier and used that instead with the required gain set to the level our smaller amplifier clipped at then that larger amplifier would be able to deliver that requested higher amplitude signal without clipping and *even more* energy would be going into the woofer. i.e. the problem here is not that the clipping is damaging the woofer but that we are simply driving it beyond its capability and a more powerful, non-clipping, amplier given that same gain requirement would have even greater area under its signal curve and thus would drive the woofer even harder.
Note that the case is different for tweeters. As the Wiki article describes, clipping the signal drives its shape towards that of a square wave and a square wave (as a greatly simplified explanation) contains a lot of high frequency overtones. This introduces a lot of spurious high frequency signals into the signal, in addition to the high notes in the music itself thus increasing the energy going into the tweeter and causing said tweeter to burn out. However this problem from clipping is a problem for the tweeters and isn't going to damage your woofers. In really extreme cases I guess it might also damage a midrange driver.