The batter has a right to stand in the box. He does not have the right to leave the box (except to get out of the way of a runner coming home) during a live ball situation. If the batter leaves the box during a live ball (and he's not running to first), he can be called for interference during the play.
Watched a Braves game earlier this year with d'Arnaud at bat. It was a planned steal of 3rd base, and d'Arnaud did his part, stood in the box, didn't move, and the catcher threw right into him trying to throw to third. No interference, even though you could tell that was the plan all along, for d'Arnaud to basically be a wall and make a throw to 3rd that much harder.