> Whereas the "real" perfect pitch people are always anchored, no matter how much noise anyone throws at them

Actually they're not immune to being thrown off, there was an experiment where people with perfect pitch were played a long orchestral piece that very slowly detuned, e.g. over the course of half an hour dropped one semitone. The study found this also detuned their sense of absolute pitch, not just immediately after but also months later.

https://www.psychologicalscience.org/news/releases/perfect-p...