Reality: The ball is NOT dead on a foul tip. Rule 2.00 FOUL TIP explicitly says that a foul tip is a live ball.
Much of the confusion surrounding this probably comes from a misunderstanding of what a foul tip actually is: A FOUL TIP is a batted ball that goes sharp and direct from the bat to the catcher's hands and is legally caught. It is not a foul tip unless caught and any foul tip that is caught is a strike, and the ball is in play. It is not a catch if it is a rebound, unless the ball has first touched the catcher's glove or hand. A foul tip can only be caught by the catcher. Thus, it is only a foul tip if the catcher catches the ball. A ball that hits the bat and goes straight back to the backstop is a foul ball not a foul tip.