Believe it or not you don't actually need to be able to read/write music to work with an orchestra, etc. I don't know whether Neil did or didn't use musical notation for this project but there are many ways he could have done it without having an extensive knowledge of music notation.
You definitely don't need to be able to read music to cover a song. All he had to do in the case of "Sexual Healing" and "Billie Jean" is figure out the chords from the originals by ear.
As for doing different versions of songs...that really doesn't have anything to do with transcribing musical notes. I think many of the songs he plays on piano live were probably originally written that way (even if they are guitar-based on the record) and again all he needs to know to transcribe them to guitar are the chords.
Listen, I really don't know how extensive Neil's knowledge of theory is and how good he is at reading/writing music, if at all, but going by a lot of the things he says in interviews and that I've read, I don't believe he relies on it a great deal. To me, that takes nothing away from him as a musician. In fact, it probably makes me respect him even more.