My middle child is the most shy of all of mine.
She would not participate in class unless specifically called upon.
In Y2 I told her that if she put up her hand and answered a few questions correctly the teacher would stop calling on her because, for the most part, teachers are looking for those that don't understand and she was, generally, not one of them.
In Y3 she told me it was because she didn't like how everyone turned to look at her when answering a question. Mentioned this to the teacher who then put her in the back row and that made it more comfortable for her.
In Y5 the teacher was pushing - a bit you like you mention. I told them that they had to accept that not everyone is the same, she doesn't like attention being drawn to her and you can't expect them all to function the same. I also said that if they wanted her to do something just tell her and she will do it (and well enough) but she will never volunteer and will say no if given the choice.
All through secondary school it's been a recurring theme - she won't participate in class discussions, doesn't put her hand up, won't ask questions. We've reacted with "oh" and "don't expect any different" as that's her nature.
However, doing ballet and tap/modern shows has made a huge difference to her. Also, helping out at the the dance school with the younger ones for lessons and easter/summer schools boosted her confidence. She also started doing drama (outside of school) and we watched with our jaws on the floor when in less than 6 months she was performing to an unknown audience (instead of parents) and did a small solo piece 
!!
Your daughter will get there with encouragement and a bit of cajoling at time. You are her advocate so I would suggest that you think about how best to do that for her when confronted with information like the teacher gave you. I'm rather bolshy and I just shut them down with 'they can't all be the same' and remind them that they only see part of their character at school.