When Does Shy Become an Anxiety Disorder?

Your instincts are good! Doing things for a 12 year old who finds anxiety provoking sets up a learned dependency. It doesn't sound like that problem has reached beyond what could be normal shyness. Your daughter may be somewhat introverted. Estimates vary from 16 to 50% of the population that some people are more socially inhibited (introverted) that others. Introverts have a lower tolerance for social stimulation, thus would prefer a handful of people to talk to rather than a roomful. A 12 year old with an anxiety disorder has trouble with age appropriate behavior, grades, relationships with friends, teachers and parents.
Your daughter's teacher says she may be a little shy. She may well have a clearer perspective given her view of many children in varying social situations including your daughter. I have to wonder: what is different about the situation when you are out with your daughter? What else is making her anxious? What could be happening is a product of that difference and without a thorough evaluation, I can only guess.
I do have to wonder if your anxiety about your daughter's struggle is feeding into her anxiety. She was already worried about talking to strangers, but now she senses your worry and her worry is made worse! How that might be manifesting in the relationship could be quite subtle. Ask your daughter about it. See if she can give you feedback about your attempts to coach her into speaking up for herself. Ask her how it makes her feel when you encourage her. Her feedback should be considered seriously. She is old enough to know what she likes and makes her feel comfortable. See if you can negotiate an approach that makes her feel more comfortable.
If she has trouble talking to you about it, take a good look in the mirror. Ask yourself: are you making her more anxious? If so, I suggest that you and your daughter go to see a counselor. There could be an issue in the relationship between you and your daughter with which a trained professional could help.
I wish you and your daughter the very best!