I think she is simply not all that fond of piano to listen to...
If so, that indicates a real problem to me, because the primary reward for playing music is you get to produce something you enjoy listening to. So if she's not doing that, all her resistance is perfectly understandable.
Maybe let her try another instrument?
Then again, piano is soooooo adaptable to so many different styles of music, and that may be the real problem. Maybe find her some musicians with similar tastes to hers? Trading fours with other jazz musicians is a great way for her to push herself both technically and creatively.
How's your Ron Burgundy impression on flute?
I find her rejection of the more technical pieces in favor of improvisational music to be a positive development, because on a deeper level it appears to be a rejection of perfectionism and an embrace of just going with the flow. I think your fears of technical music feeding into her perfectionism are well founded, so I'd follow her lead on this one.
