greymule,
There- you found
something that addresses a ball entering a uniform or equipment. Good job! I must have read right past it a couple of times.
That rule tells us that the ball remains live upon entering the uniform/equipment (ie: runners may still advance and outs can still be made).
With respect to the foul tip in question, the rule you cite combined with the definition of a catch tells us that this is a legally caught foul tip.
Under the definition of catch, we see:
If the ball is merely held in the arms or prevented from dropping to the ground by some part of the fielder's body, equipment or clothing, the catch is not completed until the ball is in the grasp of the fielder's hand(s) or glove.
So, a live ball entering the uniform/equipment of a defender remains live and may be extracted, then securely held for a legal catch. That means the catcher on our play did legally catch a batted ball that first went sharp and direct to her hands or mitt.
