I didn't have the patience to finish that, but still,
The answer goes something like this: according to quantum mechanics, at the Planck level the fabric of spacetime is constantly creating new particles, two at a time, that exist for an instant then annihilate each other in order to satisfy the conservation of matter. When this happens outside a black hole, one of the particles of the pair gets sucked into the event horizon while the other one is launched away from it. Consequentially, nothing actually leaves the black hole, but entropy is nevertheless risen.