Yes, it's easy to change teams. You just find a new manager and ask if they have openings. You don't want to leave your old team high and dry, but the only requirement was the new manager saying yes.

Obviously in reality there were most likely some negotiations amongst the managers, as the new manager wouldn't want to get a reputation for stealing people.

But I saw people change teams pretty regularly. Not just because of bad managers, but because they just wanted a new challenge.