This doesn't really have anything to do with perfect pitch. Equal vs just temperament is about relative pitch, not absolute.
Only in equal temperament does a certain frequency have a unique matching note. If given a frequency you are supposed to tell the note in just temperament, then you would also need the context - and the context is inherently about relative frequencies, i.e. how is this note supposed to harmonize with other notes. Of course you can fix the frequency/note assignment, but then you can just play certain harmonies, and others might be horribly out of tune - the whole point of equal temperament is that this is a very good approximation of just temperament if you don't want to restrict yourself to certain keys.
The "perfect pitch" ability can take on many forms.
- Some people might have "equal temperament standard modern tuning" perfect pitch, and will just tell you that everything else is out of tune.
- Some people might have "equal temperament" perfect pitch, but one week it might be standard modern tuning, and if the following week they spend 50 hours playing in a historical tuning of A=415Hz they will subconsiously switch to that tuning during the week, and will have equal temperament A=415Hz perfect pitch the week following that.
- Some people can actually tell you the numerical measurement in Hertz, i.e. they hear "300Hz" for example, and not some musical note.
Each of those persons respectively, with purely academic learning (no inherent ability required), can learn to tell you that
- If a frequency sounds too low/high for a certain pitch, then it might be correct in just temperament in some context - for example an F that sounds too high to them could be a just major below A.
- They know their tuning switches back and forth and can always relativize the note they hear to "probably a modern A=440Hz" or "I have played so much in A=415Hz recently that I'm sure this is an A in that tuning".