I had a friend at UCLA named Bill Jackson. He was a math wizard and had heterochromia—and absolute pitch. He had been a classically-trained pianist for 12 years since age 6, but said he had always recognized pitches instantly—even in the beginning. He only had to learn their names once. For him, each pitch was as instantly identifiable as primary colors are to us. He could tell you that you needed to add a little more water to your water glass to make it ring at F#. Instantly. Even if he wasn't paying attention when you rang the glass once and only then asked him.
Once I found him sitting quietly in the lounge while a piano tuner was working on the dorm piano. I had to pull it out of him, but he said the guy was doing a pretty good job—just a little sharp in the higher registers. Bill played jazz great. Loved the Ramsey Lewis Trio and raved about them after he came back from hearing them. I asked him if they were all in tune, and he said they were great. When I pressed him on this, he said that the sax was a little sharp all night, but it was still great. I dunno how he could ignore those differences, but he did.
I won't believe for one nanosecond that anyone can learn Bill's absolute-pitch ability. I've met several people since then who claimed they had absolute pitch, but they didn't know what they were talking about. If you play a note for them, and they look like they're thinking about it—even for a second—before they answer, they don't have it. It's like someone having to think whether a color is red or green.
I wish I knew what happened to Bill. He must have had a career in math because I can't find any reference to him in music.