There's truth to this as well. Bear with me for a moment if you please.You kill speakers more often with less, or not enough power.
Let's presume that an amp has no inherent limiting or clip protection. In this scenario, pushing the input signal too hard could result in a clipped signal being sent to the speaker systems. Yup, a clipped signal can overheat a voice coil.
This is why I advocate a headroom-heavy system with the proper tools for the job. You can always turn it down. If your system isn't large enough to handle the job, the temptation to push it too hard is greater. If the amp you're using has no limiting or clip protection you could fry voice coils. This is why it's so important to have big, beefy amps and know your system's abilities and limitations.
Remember, you can only get so much sound pressure from a given speaker system. Feeding it with more amp power or pushing the gain isn't going to cause it to produce more sound than it was designed to produce.