However, similar myths and misunderstandings exist in connection with that non-linearity, as with the linearity that is sought after in hifi. For example, the concept of "distortion without clipping". Clipping happens in the time domain, so it is the instantaneous amplitudes that are affected. Consequently, even with "soft clipping", which necessarily must be anti-logarithmic, the actual input range of soft clipping is very narrow, most of the time the signal is almost linear since it's below the threshold, or clipped rather hard because it's way above the threshold. Since a guitar signal has a strong initial attack and log decay, the main audible effect of clipping, is compression. As the input signal amplitude is increased, more and more of the decay signal exceeds the clipping limits and is audible as distortion.
So while soft clipping is a real thing, and pleasant to listen to, it plays a very minor role unless the instrument is played with minimal amplitude into the amp, or unless the signal is pre-compressed so the amplitude is more confined to the soft limiting zone.
But, by the time it reaches marketing and instrumentalist discussions, none of that is understood or mentioned, and it's reduced to things like "sustain" or "punch" or even more incomprehensible things like "articulation", "note separation" and so on, are used.
An actual valve (tube) amp has some subtle things going on that a generic electronics engineer wouldn't consider at first, mainly because they're used to seeing circuits work at less than overload levels. Nothing like, for example, the effect of plate voltage on a push pull circuit dropping due to a a strong input signal and an unregulated supply. Somewhere, a musician expresses that as "munch" or some strange thing that nobody can really grasp.
A lot of innovation in amps now, post DSP where you can punch in practically any sound, is focused on making solid state amps sound half decent. An actual tube amp really doesn't have much need of improvement, from an electric guitarist standpoint.
But people will always try to nurture some tenous need in order to send a product to market and profit, to do that they need to differentiate their product and that is where the exaggerated claims usually come in.