I think some may be confusing 'perfect pitch' with sense of relative pitch. If there is really such a thing as 'tone (should actually be 'pitch', I suppose) deafness', that would be the inability to recognize discordant relative pitch, and I for one don't really believe this exists, though obviously there will be different degrees of proficiency in recognizing subtle disharmony or wandering intonation. 'Perfect pitch' is supposed to be the ability to correctly identify pitches as named notes, not some extraordinary sensitivity to out-of-tuneness in ensemble, which based on my own experience is easily enough perceived even by those who don't possess perfect pitch. However, I have heard where those who do have perfect pitch ability can sometimes be driven to distraction when a piece is played in fine and consistent relative harmony, but just a bit off from what their brain tells them is the 'correct' absolute frequency of the key in question.