To say class D is bright means you are not very well versed in quality class D.
This is correct as they can be either too bright (hard) or to opaque (soft) or a milder mix of both, and it nearly always comes down to how savage the output filter is that attenuates the switching frequency. As it's phase shift effects can be measure within the audio bands upper frequencies right down to 5khz, especially, the "opaque sounding one". You never hear of anyone criticizing the bass, that's because it good!
There are those that for the life of them can't hear anything wrong, good luck to them I say.
Cheers George