This is just not true. It's got nothing to do with fake news, in fact, the exact opposite. Dirt Sheets are literally the name of wrestling publications. They weren't fake in the past, they aren't fake now. The "dirt" refers to the breaking of kayfabe by them, as opposed to the regular wrestling magazines of old that kept kayfabe and reported as if it were real. The "sheet" refers to the fact they were printed on A4 paper sheets and distributed like newsletters.
The WON, PWT, PWI, F4W, and the many websites that feed you the news that originates from them are all still "dirt sheets" and that has nothing to do with fake news or any other kind of media thing that people have thought up over the past few years. It's a term that's been around ever since the WON was created.