Many of the responses to this comment imply that this is something fundamentally different than perfect pitch and give it some different name ("pseudo absolute pitch", "perfect relative pitch", etc.). While I concede that most people think of perfect pitch as something that is instilled in some way in early childhood rather than achievable through practice, I guess I would ask those commenters... why do you think the latter is fundamentally different, or is using some separate mechanism?

There are many skills which are much easier to instill in early childhood and are simply harder to master if approached in adulthood -- language learning, certain athletic skills, and more -- but we would never consider any of these impossible to achieve through study. Sure, maybe the maximum achievable skill level is less than what could have been possible if study began in early childhood, but we would not say that it is impossible for adults to achieve a level of mastery, or that those who gained a skill through serious practice must be using some separate mechanism than those who learned it in early life.

I contend that it is the same with absolute pitch. After all, there is not even a perfect level of absolute pitch mastery! In layman's terms, "perfect pitch" is usually understood to mean that a person can immediately name a pitch when played -- on a 12-tone western music scale. But some people people with perfect pitch have better precision than that and can estimate quarter tones, etc. If a note is played that's 20 cents sharper than Ab, and person #1 says "that's an Ab" while person #2 says "that's a note a touch sharper than Ab", most people consider neither statement to disqualify them from having absolute pitch. But there is a difference. Moreover, no person on Earth can name a pitch down to, say, a couple decimals of absolute frequency value. Doesn't this imply that the skill exists as achievable points on a spectrum, not as a flat binary?