Ack...my ds is doing something similar! He's very social, but when it come to answering questions or "showing" his teacher his mastery - it's as if he doesn't trust himself. I wish I had answers. His teacher is NOT on board.
I would make sure an application to the G/T program identifies this issue - if it is anxiety, that is a medical issue - which brings ADA laws into play.
That's a good idea, mentioning this in the application. I definitely think whatever it is has to do with either her fear of failure, perhaps she isn't confident, or perhaps her daydreaming... And I wouldn't be surprised if she is afraid she would hurt the teacher's feelings if she told her she already knew something. She is very sensitive to other people's feelings.