That's true, Roger
To be fair, of course, no properly operating audio amp should have audible harmonic distortion.
It's also true that all humans (even ones who can't hear the difference between A and A'') feel genuine discomfort when third order harmonics are audible. Fourth and fifth order harmonics are pretty much negligible even in a bad SS amp.
Second order harmonics can be used in moderation to produce a pleasant sound and it's really easy to do this in a tube amp without increasing the third order harmonics to audible level. It's much harder to do in a SS amp (yes, darlings, MOSFETS, we know).
Clipping, of course, is the real problem facing SS equipment designers. Not only are tubes inherently more linear at real-world volume levels, their clipping artifacts are less horrid when transient than SS.
While, on paper, one can make the argument that skew (or attack or rise time or whatever term makes you happy) is equally good in a really well built SS amp and a really well built tube amp, there's no way around what really good testing equipment shows: Tubes attack faster and one needn't fight the 'ring' which haunts SS amps with super fast rise times.
I suspect, though, it's the cross-over distortion of badly setup/designed SS amps which people are 'hearing' and causing them to prefer Class A tubes. Who wouldn't?