I could be wrong, but high 2nd order harmonics play tricks on my brain's perception in favorable ways; it gives an exaggerated sense of space, and seems to flesh out the various parts which compose the sonic image. An amp designed to produce distortion which emphasizes the second harmonic and has otherwise non-objectionable distortion spectra could indeed image differently that your average mainstream amp with better specs. Using the First Watt mentioned before, in the same room, with the same source, speakers, and layout, changing the amps did indeed change the imaging; subjectively, more depth-of-field, noticably more 3-D. It was distinct and unmistakable, if not night and day, and the only difference was the distortion characteristics of the amps. [Now cue the discussion about wheather such devices qualify as amplifiers, or are merely expensive sound processors.]
Unfortunately (or, if you're evil, fortunately) most of the gear that behaves like this is audio-jewelry class expensive, and you're stuck with the particular sonic taste of the designer of the amp, rather than accurate, linear reproduction. But this gear is out there, and some folks really dig their distortion.
But aside from amps specifically designed to imprint their own sonic signature, what you say is absolutely correct.