Not sure what you don't agree with. Firstly, your comment "The power supply is 100% in the signal path in almost all audio amplifier designs" is completely wrong at all levels.
Now you are saying something different. You are now alluding to different things.
OK, please show. Without an actual example, this is an anecdote.
Again, please show.
Well, let's read some posts about psu design for amplifiers.
In any well designed HiFi amplifier, there will be a power supply whose job is to convert the AC mains supply voltage to a DC voltage. The power supply must also be able to provide a reserve of power to cope with any sharp transients in current demand without suffering a decrease in voltage...
www.audiosciencereview.com
In the EETimes article, by using a regulated voltage supply instead of an unregulated voltage supply "Clipping behavior will be cleaner, as the clipped peaks of the output waveform are not modulated by the ripple on the supply rails. Having said that, if your amplifier is clipping regularly you might consider turning it down a bit."
That right there is a change in sound quality.
And a clue: "...the clipped peaks of the output waveform are not modulated by the ripple on the supply rails."
Power supply ripple modulates the audio output waveform.
[I know this is an engineering problem that has been solved, but the point I made was that the power supply is part of the signal path and has influence on the audio output, meaning that if you hobble even the best audio amplifier circuit with a poorly designed, noisy, high impedance power supply, the sound quality from that 'best' audio amplifier will definitely suffer, first objectively (measurements) and if bad enough, subjectively too.]
I once had a simple push-pull 300B tube amp rigged up, with an external power supply. I made a giant regulated supply using a 6336 pass tube and a 12AX7 differential stage as the error amplifier, along with an 0D3 as a voltage reference. It changed the sound of the amplifier in subtle ways, but bass was tighter with the midrange sounding less 'tubey' and more like a very good solid state amplifier. I could jumper out a few things and switch it back to an unregulated 'passive' power supply, which absolutely increased the power supply impedance. The resulting sound was more in line with what you'd expect from a vintage tube amplifier, with that more ill-defined, slightly woolly bass and what I thought was a more tubey sounding midrange (although I admit that was probably my own biased opinion, not based on real differences I'd stand by now).
At one point I tried to lower the B+ voltage by adding a high power/low value resistor in series from the power transformer center tap to ground, which did lower the B+ voltage but also really raised the power supply impedance. I could really hear that! The bass got all bloated and loose.
All that's just anecdotal, I know. But it was an experiment I ran for myself to prove/disprove effects of power supply impedance on a simple push-pull triode output stage.
Anyway, the articles I linked to answer the question. Please read them and quote whatever you like to disprove any points I've made or prove any points you've made. The whole point is to try to be 'scientific' here on Audio
Science Review. Right?