You are played two clips: one sounds a hair different. Who wouldn't think, "hmmm, I wonder if there is really no difference here and I am imagining it."
All those who would think they're being asked to identify one or the other and will, therefore, hear one. Frankly, I think that is the much more likely error than the one you've described, unless you're using audiophiles or "trained" listeners who understand what the test is trying to show (and by that I don't mean difference/no difference, I mean that all amps sound the same, etc). In any case, these are precisely the kinds of errors that are overcome by exceeding the statistical margin for error. And this kind of testing has been used successfully for decades in all kinds of A/B identification and preference testing for all kinds of subjective (and otherwise) tastes, touches, sounds, smells, etc. No one has ever come up with a decent reason why audiophile equipment is an exception.
Tim