I'm an example, acquiring AP when I was about 42. . .one day listening to some music I became aware that every time I heard a "b" I knew exactly what it was. It was not like knowing a pitch by remembering the last time you heard it;
I believe this is an example of what in the literature (going back to Bachem, 1954) is referred to as "quasi-Absolute Pitch," which is, by definition, when a person has "AP" for a single note or two. "True" AP possessors can label or produce any note. It's not clear from Eliot's description if the other notes he eventually acquired were identified with reference to this first note, in which case he has AP for a single note and used his excellent sense of RP (relative pitch) from there. If in fact Eliot acquired it, he would be the only case I know of an adult who did.
Check http://www.perfectpitch.com. They claim that many people have acquired perfect pitch with their method and cite two studies in which it= s effectiveness has been confirmed: (1) Rush, M. A. An experimental investigation of the effectiveness of training on absolute pitch in adult musicians, The Ohio State University. (2) Nering, Marguerite Elaine. A study to determine the effectiveness of the David Lucas Burge technique for development of Perfect Pitch, The University of Calgary.
I'm aware that David Burge and this method claim effectiveness in adults, and that they cite these two papers. But if you actually read those papers you'll see that the results were inconclusive.
Dan Levitin