It is evident that this kind or argument can be inverted. People as Hawking, experienced in black holes and general relativity, can say nonsense when entering in the field of thermodynamics.
Even if we ignore now that «the energy that is in the gravity field» is not well-defined in general relativity, what you say about thermodynamic energy and gravitation seems to be without any basis.
Already many ordinary textbooks explain how gravitational energy [itex]M\phi[/itex] contributes to thermodynamic energy. Of course, in a BH the situation is more complex and [itex]M\phi[/itex] is not enough, but thermodynamics in presence of gravitation continues to hold and I fail to see your point.