The ability to remember music is more like chessmasters being able to remember configurations of the chess board who can remember any chess board configuration but suddenly become like any of us when trying to memorize an impossible configuration.
It is, for example, unlikely that Mozard would have had instant recall for Indian music that has many rhythms, 22 tones in an octave and some very different harmonic constructions.
Essentially a well trained ear can remember the music, but not the sound.