I’m far from a professional musician, but I find it difficult to believe that the written music for a solo pianist serves any purpose other than perhaps a bit of confidence in an emergency if memory fails. Surely there’s no way you can actually read complex passages anywhere near fast enough to actually rely on them for a live performance.

His sense of absolute pitch shifted in later age, leaving him constantly unsure as to the correctness of the notes he was playing. The music was intended to be a check against any confusion arising from this. At least this is what he claims. Would be interesting to know if this was necessarily entirely psychological or not.

IIRC he forgot a note one performance and put the sheet music in front of him ever since.

It is easy to imagine forgetting which high or low disconnected note you're supposed to start a passage from on a piece you haven't played recently -- or you have the sense of the feeling of a note but might be off by a fourth.

When I play guitar while reading sheet music or tabs, I often glaze over what's actually on the paper or on the screen but still "read" it faintly -- Take away the guide or make me look at my hands and I'm helplessly lost, however.

I have a pet theory that it's more about flow and some kind of vision-muscle memory.