As I wrote below, the Joyce Hatto story is partly based on understanding that much music isn't just about the musical sounds; it's about the performer and our appreciation of his/her efforts to scale mountains of notes. This is more humorously illustrated in this wonderful bit from two musical comedians I'd never heard of. Never was a big fan of Viktor Borge, but these guys make me laugh.
Anyway, the idea that this pianist supposedly needs extensions to get all the notes covered in Rachmaninoff's most famous piece shows us again that as listeners we 're interested not just in the musical sounds, but in the technical gymnastics that the performer must go through to make the sounds. Although this particular piece doesn't really require huge hands, its appeal is partly based on the way that it exploits the full sonority of the piano and gives the audience the sense that the pianist is swallowing the instrument whole. I can still remember looking at this score for the first time and being overwhelmed by the sight of four musical staves bound together as one. One could even say that the visual of the score is part of the meaning of this music and certainly the visual of the pianist reaching back and forth across the keyboard is part of the meaning. We simply wouldn't get the same effect if two pianists played this work with four hands.
It's an interesting idea, this concept that a physical constraint changes the way we hear music. Like many other piano teachers, I often find myself telling a piano student to feel a large melodic interval the way a singer might feel it because of the physical sensation a singer experiences when reaching for a note an octave or more above. The assumption is that a good listener will also feel the vocal expanse of the interval if the performer suggests it effectively, even if the reach for a pianist is trivial. Although the humorous performance linked to above isn't intended as a real interpretation of the piece, I found it quite interesting just to listen to it without watching the silliness as the pianist waits for each new chord extension to be handed him. Hearing those excruciating pauses actually communicates something real about this supposedly hackneyed piece. The physical struggle matters in music such as this.