Her science-oriented methods break down when it comes to (in the broadest sense) “supernatural” phenomena - because they are, by definition even, outside science.

I only watched the first 2 or 3 seasons of The X-Files, so I there’s lots of episodes I haven’t seen, but this seems incorrect to me. Scully and Mulder were chasing unexplained phenomena, which are entirely within the realm of science. Humans tend to call things “supernatural” when we don’t know how to explain them (ghosts, fairies, aliens, etc), but those entities (in the context of The X-Files where they are actually real), once observed, can be subjected to the scientific method the same as anything else. Aliens in The X-Files aren’t magic; it’s just extremely rare for humans to be able to observe and study them.