I know I'm not the brightest bulb in the lamp but what exactly does that phase shift mean in the link from George?
Phase shift is interpreted by the ear as a tonality depending on what is causing the phase shift- a rolloff at high frequency outside the audio band can sound like a darkness, it can also sound like a brightness if there is a peak. The ear uses phase information for echo location, so it can alter the soundstage too. The ear is entirely insensitive to phase at a single frequency, like a sine wave or the like; and there are other factors it uses to sense tonality and soundstage, so even though phase shift plays a role, its not the only way the ear works. But if you really want to get the tonality and soundstage right, this is a thing that needs attention.
While some class D amps have significant phase shift, others do not, just as in traditional amplifier technology. It is a logical fallacy called 'Guilt by Association' that is being employed here by George- he is saying *all* class D amps have this phase shift in the link he provides, when actually the curve is for a very specific amplifier. Logical fallacies are inherently false and this is an excellent example.