Batter hit with a foul batted ball = foul ball. If a ball hits an object foreign to the ground in foul territory, and the batter is foreign to the ground, then it is a foul ball. This is the same reason why a runner hit with a batted ball in foul territory is a foul ball, but a runner hit in fair territory is out (unless the ball passes a fielder, or the runner is occupying a base (only in softball)).
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