Absolute pitch is the ability to correctly identify any musical note. It is close to another ability, relative pitch, which is the ability to identify any interval correctly, although relative pitch is usually described as the ability to correctly identify any note, once the subject has been given a "reference tone". An important fact here is that relative pitch is not as rare as absolute pitch, which may hint that absolute pitch is harder to acquire/train.
What kind of learning procedure would you design to learn absolute pitch?
In particular, I have two strategies in mind, and I don't think either would work. The first one is simple: a computer produces a note, the user identifies the note, the computer corrects the user. This is flawed because the first note in pair with the correct answer given by the computer provides a reference tone, therefore, after the first note, the user only trains his/her relative pitch. The second strategy would be to not correct the user immediately, but instead wait for example 10 notes before correcting. This seems flawed too, because of how crucial a quick feedback is to learning. Note that, with either strategies, it is not possible to make long learning sessions anyway, because it soon becomes a relative pitch training strategy.
Any clever idea?
I would claim that this guy essentially goodharted himself into passing this online test. If you train for a month using always the same small set of clean single-note audio samples, of course you'll end up distinguishing them. This is like building a neural net which solves just MNIST and writing "we achieve full handwritten characters recognition" in the headline.
Also, note that the online tool he uses doesn't let you hear the next note until you've correctly guessed the previous one, and this sort of feedback makes the exercise significantly easier (after the first note you could basically achieve near 100% accuracy with relative pitch alone).