It's obvious having a department to investigate unexplained shit would come back and bite them in the ass if the government is responsible for a lot of said unexplained shit.
"It was all for show, they didn't really think Mulder and Scully would accomplish anything!"
Then why even leave it to chance? Why not just have the X-Files exist only on paper with no resources allocated whatsoever? Or if they have to make more of a show of it, just assign two glowies who are already in on it and just follow a script that never points back to the deep state.