from the Wikipedia page: "Perfect pitch ... occurs entirely at random in about one in every 10,000 of us,...."
it has to be more than that. I have it, my sister, with my coaching, learned it. I think anyone with relative pitch (which anybody who can carry a tune has) can learn perfect pitch---though it's easier if you have "bad ears"---seriously! since different pitches would actually sound "different". I actually had to teach myself----After playing in HS band for a while, I realized I had our B-flat tuning note in my head. So I tested on piano, it was really an A. I did this for a few weeks and it settled down and I could imagine a B-flat, play it, and get a match. Went about 12 years without doing much music, and nearly lost it, but joined a community band, and it came right back---again starting with our tuning note, B-flat.
So, my opinion is perfect pitch is hearing notes repeatedly while knowing what the notes are (like the b-flat tuning note). A good crutch is a piano with some notes that sound funny---recognize them immediately---and with practice you stop depending on the crutch.