Exactly. That's why argument to authority fails. In this situation, I think Hawking is right.
It's pretty simple. Gravitational potential energy makes up a substantial amount of energy in astrophysical objects. Hence arguments based on energy conservation that ignore interactions of the gravity field just don't work. If you introduce the gravity field, the situation that Hawking finds is pretty standard.
My point is that adding gravitation introduces additional terms into the energy equation, and once you introduce those terms, the arguments in the paper break down. The paper makes arguments that ignores the impact of gravity on the thermodynamic equations, and you just can't do that.
Gravity changes everything. Once you have a gravitational field, then adding or removing energy from the system will cause interactions with the gravitational field, and *that's* what gives you heat capacities that you don't see in non-self gravitating objects.
Black holes are not monoatomic ideal gasses. Because of self-gravitation, black holes are different enough so that you can't even use monoatomic ideal gasses as an analogy.