One of my long-time students is a young man studying computer animation at the School for Visual Arts. We both know that he is not the usual piano student--whatever that is. He approaches the piano as a composer. In fact, I learn from him how Beethoven might have approached the instrument: that's how objective and responsive his ear is! A pretty high standard, wouldn't you say?
Why do I insist that we get involved with the smallest detail in his awareness of music, since we both know that when he plays for people it really doesn't matter that he will inevitably play wrong notes? He needs to know that composers write music one note at a time. Everything is there for a reason, though the reasons are not necessarily obvious, especially in the case of a truly great composer. Maybe that's how we know a composer is truly great.
This student is learning to respect the detail in his own creative work and in his reactions to the work of others.
Case in point: I heard a performance of improvisatory music the other day. I am haunted by a G# that had no business ending a piece in D except, perhaps, to haunt me.