No, but it is worth being careful about what such fitting means: What it's saying is "given this set of theories about what the black hole might look like, here

No, but it is worth being careful about what such fitting means: What it's saying is "given this set of theories about what the black hole might look like, here's what it most likely looks like" (and hence what theory of those in the set is most likely). That's still usefully improving your knowledge, even though in theory there could be some other shape it looks like with theories you have not considered. And stating with the prior it could look like literally anything is not necessarily reasonable: no-one expects that it would look like a tree, for example, and that's because of other things we have observed about the universe. Science, especially astrophysics and cosmology, is a lot like a gigantic crossword: the clues and answers to other parts of the puzzle constrain the other parts, and while it's theoretically possible that there is some completely different model for everything that fits all the observations done so far, generally the bits which are less clearly known still have a pretty well-defined shape, because they are constrained by other information and the models which fit that.