He proposes that pianos produce overtones that are at a slightly higher frequency than the precise harmonics. So when piano is playing on an amplifier that has rich even harmonic distortion, you hear both the precise harmonic from the amplifier and also the slightly higher frequency piano overtone, at the same time. This causes them to "beat". Simple but very instructive explanation from a no snake oil company.
This would then imply that amplifiers, even without going into clipping will result in audible differences.
It is easy enough to record “middle C” with numerous digital pianos to see if that’s actually true.