In a recent episode of 'Supernatural', Dean Winchester said, "'The X-Files' is a TV show. This is real!"
Even though 'Supernatural' and 'The X-Files' should be sharing the same TV universe, I don't think that line has to be considered a Zonk. (For those just joining us, a "Zonk" - an old term from 'Let's Make A Deal' - is a discrepancy in which one TV show refers to another one as a TV show, even though they both share the same world.)
In "Hollywood A.D.", an episode of 'The X-Files', a movie was made that was loosely based on the work done by the FBI agents who investigate those cases that are classified as "X Files". In another episode "Jose Chung's From Outer Space", a roman a clef novel was written by Mr. Chung that was also loosely based on the work of Agents Mulder and Scully.
Either one of these options could be considered as the basis for a TV show that dramatizes the X Files cases. If the movie did boffo box office, it would stand to reason that somebody would develop a TV show based on it. The same could be said for "From Outer Space", the book by Mr. Chung. (And although macabre, Chung's murder in an episode of 'Millennium' might have heightened interest in creating a TV show based on his work.)
Whether or not this show would have the backing of the FBI, as the old series 'The FBI' did, I can't say. (But I tend to doubt it.)
So no Zonk here. Dean Winchester obviously saw this show based on the "real life" X-Files work of Fox Mulder and Dana Scully.
No other information was given, but I think it's safe to assume that the characters in the Toobworld version of 'The X-Files' were dramatizations of the two agents. The names "Mulder" and "Scully" have popped up far too often in other TV shows to bother dancing around the possibility here.