I am a professional musician (bassoon player in a symphony orchestra). I can, if I practice it a couple of times a week, achieve and sustain perfect pitch. I had no semblance of perfect pitch until I decided to practice it at age 24. Before that the only chance I had to guess a note was to put in in relation to my own voice. Even though I don't practice this anymore (it isn't very useful), I still often just instinct…
The TA in the course would often talk about the concept of "pitch memory", both absolute and relative. In other words, perfect pitch isn't a binary concept of you either have it or you don't, but it's your ability to remember and reproduce absolute pitches from memory. What we think of as "perfect pitch" is the extreme version of this, where your pitch memory is basically long-term and you can sing a middle-C on command. But many people have decent short-term pitch memory. One girl in my ear training session (a pretty accomplished cellist) could remember absolute pitches for the whole 1.5 hour session; if we came back to a note, she could get it, but she was usually lost in the beginning of the session when we came in cold. I (9 years of violin training, starting at age 7) had a pitch memory of about 5-10 minutes - while we were working on a specific interval, I could remember and reproduce the base note without being prompted by the piano, but once we moved on to another interval I'd lose it. My wife (no specific music training) goes off-key after about 20 seconds.
It wouldn't surprise me that training this ability when you're young leads to much longer-term memory than training it as an adult, the same way that training gymnastics when young leads to the ability to do a back handspring from muscle memory, or training a foreign language gives you a much better ability to speak it without an accent.