You'd drive through a gap that was getting smaller at 100mph? Yes, there was just enough room, but Paul wouldn't have known exactly where Lewis's front wheel/wing was going to end up.
Nobody drives though the gap that EXISTS, but through the gap they think will exist when they get there, so he had to go to the grass.
Can't take anything away from Button for the team making that call though. But Lewis, apparently, made most of his tyre calls, and he's never made a good one yet.