I have a kid kind of like this. He actually has no problem with public speaking and is anything but shy. He just has no interest in comparing himself with anyone else. I've noticed it drives some other boys his age nuts that's he's very ahead academically but won't banter about it. He does non-competitive athletics even.
I would let it go. I think she probably learned quite a bit from this experience. It might help to talk to her teacher about it and ask that she or he might encourage her into some opportunites. My son has a piano teacher that regularly gets him excited about auditions and contests. Not as a competition with other people so much, but as a way to push himself to a deadline and/or goal. Which has been a very useful experience. I think there is a difference between finding your "voice" and confidence, and being a really competitive person.
Good luck!
