Sorry about the perceived attitude. I don't see it so I can't fix it. It's strange coming out of the blue in your reply. I can only say if it bugs you we shouldn't exchange.
I don't follow. Why do you *have* to do the math? Where in the math will it explain matter/energy coming from the black hole? Applying math to physics is based on principles that are deduced from observations. Understanding math without understanding the principles is not understanding in my book.
I watched the video now and you are sort of right. He doesn't explain the mechanics of how the matter/energy of the black hole decreases, but he specifically addresses it when he says, the matter of the black hole only consists of a surface and the matter/energy comes off that surface. He seems to be saying that because the matter never *appears* to an outside observer to fall into the black hole, it *can* escape without violating any principles. When some discuss the singularity inside a black hole, it would seem it is not obvious that there *is* a singularity. If there is, how did it get inside the event horizon and how could that matter ever get back across the event horizon?
Analyzing the process by thermodynamics is applying a well known principle to a much less well known situation. We have no reason to believe our laws are immutable for all time and space.