It's perfect pitch for a certain agreed standard, which has been defined by international agreement at present as such and such, and not so and so.

The same way that there is an agreed length for a metre and a yard, which could have been completely different lengths, just so, the definition for notes could have been completely different. And has of course been defined differently at various times and places.t

"Perfect pitch" is a matter of having learned how to recognise the arbitrarily defined notes. That's why I said "absolute pitch" is a nonsensical term. I sometimes wonder if people with perfect pitch could adjust to cope with a changed definition of notes. I suspect in some cases they might be able, but probably not too many could in adult life. Maybe the drugs could help...