Agreed. If we insist on starting from science and then say the problem is insoluble, we are in effect saying that science is the solution for all soluble problems. How is that not scientism?
Yet even to hint at other valid solutions for the problem, eg from theology, is to say that “a complete scientific explanation” is an oxymoron. If one concludes that the whole of biology tells you nothing definite about the nature of inorganic chemistry, you have only shown that biology is an inadequate explanatory tool in that area, and need to ask why. In the last case it’s pretty obvious.
Regarding science and divine action it’s a little more subtle, but must include the fact that the metaphysical model for science excludes divine action and some of its necessary components, such as teleology. It can be staring one in the face, but hidden because of the spectalcles you’re wearing.
Quite aside from divine action (where there is a real dichotomy between what happens within creation and what happens in its creation - a matter only approachable via revealed theology and, to a limited degree, philosophy), we need to ask why our science should also exclude as “not scientific” things that are both natural, and created, such as human will, intentions and reasons.
Conversely, if we believe that will, intentions and reasons are not opaque to science (and if outside the purview of the physical sciences at least within that of psychology), then it’s not clear why the results of divine action in the natural world should not be admissible within science, if not their modality.