I think the nature of the fidgeting is important here. If he's just squirming around, minding his own business, the teacher has no reason to complain. But if he's moving around, dropping things, making noise, turning around in his seat, and distracting the other kids, then there is a problem. DS7's teacher told me that this is a very common thing among gifted kids. In fact, he tends to wander around the room while he's reading, and half the time when he's reading at home I find him upside-down or half-off the couch, but still engrossed in his book.
If his boredom is getting to the point that he is distracting others, perhaps you need to give him something to keep him occupied. I bought DS a spiral notebook, and I write math problems, grammar, and words to alphabetize in it. He doesn't work on it every day, but he keeps it in his backpack and takes it out when he has extra time and needs something to do. It gives him a bit more of a challenge, keeps him occupied, and makes him feel like he's actually accomplishing something at school.
