For ancient solid-state amplifiers this may well be true, but in modern 'accurate' solid-state amps all harmonic distortions are orders of magnitude below what is audible. Now tube amps on the other hand are often designed with intentional high harmonic distortion for a euphonic sound.
While I agree that a lot of SS amplifiers do exhibit the behavior you are talking about, I suspect these harmonics are audible (I can hear references tones at -90 dB in my system on a quiet night):
Not wanting to disagree, just pointing out that I feel their are some exceptions to the idea that all contemporary SS amplifiers feature inaudible levels of harming distortion.