I did see that recommendation once in an old Tannoy manual, for the HPD series, that you should match the speaker power rating to the amplifier power rating. The problem apparently is that many integrated amplifier manufacturers have their maximum pre-amp volume level far too high, so that if you did turn it all the way up, the (integrated) power amp would clip.
Nowadays, the speaker manual normally suggests how powerful the amp should be, e.g. 25 - 175 watts. If the amplifier does clip, the sound will be harsh and grainy, and if you put it up even higher, the tweeter may blow.