Perfect pitch is a simplification, it's not really binary like you either have it or don't. People have varying ability, practice, and speed at identifying a no

Perfect pitch is a simplification, it's not really binary like you either have it or don't. People have varying ability, practice, and speed at identifying a note relative to a reference, and "perfect" is how we describe being past some threshold. When we talk about perfect pitch we're usually assuming 12-tet tuned to A440 but you correctly homed in on the "problem" with perfect pitch. Is that C a little sharp, or did they just tune to A446 for some reason? Just intonation, microtonal scales, there are a lot of notes out there. How do you know they're "wrong" and not just trying to play the note that sounds out of tune to your ear. "Perfect" has to be established against some intention, we just usually assume 12-tet A440. Anyway the ability is at least somewhat a matter of practice and training, so you can develop it against any consistent reference, regardless of the tuning or intonation system.