don't believe that about too little power. It's not true.
Now, to speculate on your situation: Small speakers, like tweeters, cannot handle as much power as a larger, more robust speaker such as a woofer, or even midrange. When individual speakers are combined into a system, they may rate it as x watts power handling, say 100 watts, but the woofer may be rated at 100 watts but the tweeter may actually be rated at ten watts or so.
A crossover network takes the music, divides it into several bands, and then sends each respective band to the speaker beat able to handle it. So, at any given time, one speaker can be very active and another virtually silent.
I know that album. I know that song. Very Well. That SACD is one of my demo discs. When those chimes kick in, and they kick in LOUD, they can send a tremendous amount of energy to the tweeters. My $$ are on that was what happened. All that music is concentrated in high frequencies and harmonics and virtually all your amp's available power was sent to that poor tweeter and that was too much for those little guys to handle.