I think that the Season 3 episode "Fly Boy" was arguably the best X-FILES parody any show did at the time.
That brings up one of my favorite bits of silly writer trivia: the guy who wrote that episode, Jeff Vlaming, was hired a few months later as a staff writer for The X-Files. Which means that an X-Files parody for a cable sitcom ("Molly, in 1959, three Soviet Georgian Yak Herders inexplicably burst into flame") was one of the last things he wrote before joining the actual X-Files.
There's at least one other case I can think of where something like this happened: Arnie Kogen, the veteran comedy writer and Mad magazine contributor, wrote a parody of Newhart for the magazine in 1983 and was hired as a writer for the retooled Newhart three years later.
There must be other instances where someone was hired for a TV show after having already done a parody of it, for a sketch show or something like that.