We use psychoacoustics so that we don't have to run out and perform double blind tests every minute. I explained why perceptual masking does not help you here. You can't counter that with "I don't think so" and demand a double-blind test.
Look at this graph:
That high distortion goes way down to 20 Hz as it should since the circuit is operating well outside of its design metrics (due to amp clipping). So -now take that 1 kHz tone and move it down in frequency such that those harmonics land in 2 to 5 kHz. Then look at Fletcher-Munson curves:
See how the thresholds for hearing anything there is actually negative SPL? And therefore way way lower than the harmonics we are seeing here?
Those harmonics keep going higher where the amplitude of content is very low. It mixes with them and potentially makes them higher pitched.
So your skepticism is not based what we have measured and what we know about science of what we hear.