I had a bass player in my group who had perfect pitch.
And he explained to me how it is as much handicap as blessing.
For most of us, tuning an instrument up or down a little is no big problem as long as the instrument is in tune with itself. Most people have "relative" pitch understanding and automatically adapt their singing to the pitch of the instrument.
But for those with perfect pitch it's a disaster if the instrument is not tuned to concert pitch (A=440 hz).
They hear every note of an instrument that is tuned above or below concert pitch as "wrong".
They cannot switch to "relative" mode. They are locked into perfect pitch.