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.