Perhaps we could say this is too simplistic? Or just outright wrong. This approach seems to reject observations (a huge part of science). We can prove observations (are real), but we might not be able to prove any theory explaining those observations, and thus we make assumptions. I don't think this falls under metaphysics, does it?

Probably.

Yep that's basically true. We all have to accept certain things as givens before we start. As in mathematics where they are called axioms. The most important of which, beyond pure maths, is that we all have to accept the idea that the only input we receive, that from our senses, is not a total illusion, for if we don't accept that then nothing is true and we are going nowhere, except into empty aimless solipsism.

The idea reflects however on the big mistake however that many religious apologists then make, which is to confuse the acceptance of practical axioms with faith. But they are quite different in that axioms, though without any basis in evidence, are things that you accept because you have too, especially where you have no choice, so that they could be called necessary faith or axioms. Whereas religious faith is used when there are choices, elective faith. And that difference is not just a practical mater of how we work things out, but actually changes the whole nature and meaning of the acceptance. So much so that the two things should probably have different names and it is an unfortunate accident of history that in English the word faith has been applied to both. The language needs revising.

Apart from math, science doesn't PROVE anything. There is always doubt/error-bars/new-ideas. It can disprove things.