Sure, there also have to be rules about how the mathematical quantities in the model correspond to physical quantities that are measured in experiments.
> It is based on theories which acquired their epistemic weight elsewhere to lend to the problem being studied.
Translated into plain language: you can take a physical model whose predictions have been confirmed over some range, and extrapolate it outside that range. Sure, physicists do this all the time.
But that does not mean that the extrapolated predictions are automatically correct. You still have to test them.
> Conclusions made about black holes are made on the basis of QFT and general relativity, unlikely to be overturned so long as the researcher is working far enough from the singularity for the idea of doing QFT on a fixed background spacetime to still apply.
I understand this is a common belief among physicists. That doesn't change the fact that, unless and until we have actual experimental data, these conclusions have not been confirmed.
Also, what is involved in black hole formation and evaporation is not "QFT on a fixed background spacetime". Quantum fields make non-negligible contributions to the gravitational source in these models. That means that, for a fully consistent model, you need a theory of quantum gravity, which we don't have. The actual framework being used basically assumes that a spacetime geometry sourced by the expectation value of the stress-energy tensor of the quantum fields is a sufficiently good approximation. Which is still an assumption, no matter how many physicists believe it, unless and until we have actual data to test it against.
Importantly, I don't think this is true. The gravitational field at the event horizon of pretty much any black hole people care to model, is actually quite "weak", when compared to the Planck scale where quantum gravitational effects are expected to become important. While quantum gravity would be needed to model phenomena deep inside a black hole (near what is referred to as the singularity), phenomena at the event horizon, such as Hawking radiation (and presumably, the phenomena these researchers claim to predict?) can be modeled quite adequately just using QFT and classical gravity.
More precisely, the spacetime curvature at the horizon of any astronomically significant black hole (i.e., one of stellar mass or larger) is quite small--many, many orders of magnitude smaller than the Planck scale.
While this is true, it's not what I was talking about. Black holes get formed by gravitational collapse of massive objects. The models of that collapse process that were current in the 1970s, when Hawking published his original paper on black hole evaporation, were purely classical. Since then, particularly in the last decade or two, there has been a lot of theoretical work on non-negligible quantum corrections to the collapse process. Not having to do with quantum gravity, but just ordinary quantum fields (like those in the Standard Model) providing corrections that were not known when Hawking's original paper was published, or for another two decades or so afterwards.
Also, even in vacuum, quantum fields (again, not quantum gravity, just ordinary quantum fields like those in the Standard Model) can provide non-negligible corrections. The most obvious one is a nonzero cosmological constant, aka a nonzero vacuum expectation value for the energy density of the "ground state" of the quantum fields. The accelerated expansion of the universe indicates that the cosmological constant is indeed nonzero, but the value implied by those observations is about 120 orders of magnitude smaller than what our best current understanding of quantum field theory gives us. So obviously there is something important missing in our understanding of vacuum quantum fields.
Finally, to get to the main issue I was referring to in my earlier post: the problem with having quantum fields as a source of gravity has nothing to do with the magnitude of the spacetime curvature, it has to do with having superpositions of different quantum field configurations, which means superpositions of different stress-energy tensors. You can't handle that with a fixed background spacetime; there would need to be a superposition of different spacetime geometries. Which requires a theory of quantum gravity.