I myself have perfect pitch and I don't feel cursed because my upright piano has been slowly getting out of tune over the years. I have genetic perfect pitch. In other words, it is my DNA and not my ear training that caused me to have perfect pitch. I can hear pitch in noise and tell exactly what pitch and octave it is in. Other than the difference between violin and viola where it is only at low notes that I hear a difference, I can tell exactly what instrument the note came from.
If anything, I think that perfect pitch is beneficial when it comes to an instrument being out of tune. If you have relative pitch, you could adjust it sure but you might not get the pitches right, just the relations. If you have perfect pitch, you can tell exactly how much it is out of tune and in what direction and adjust it accordingly so that it is at exactly the pitch needed.
I have tuned a guitar a few times before and have always been able to get it to the right pitch. I get 2 strings in tune and then I get a third string in tune and it knocks the tuned strings out of tune. I keep going until all the strings are in tune. In this case, perfect pitch is extremely helpful.
So why does everybody say that a drawback to having perfect pitch is knowing that an instrument is out of tune? Is it really a drawback when in fact perfect pitch is extremely helpful to get the instrument back in tune?