Alex Jones/Infowars is constantly smacking people in the forehead through shortwave radio broadcast from WWCR every weekday.
/s
With more substance I guess we could start looking up FCC standards when it comes to broadcasting lies over the air.
They gave thousands of licenses to iHeartMedia (Clear Channel) in the 90's, which now broadcast Rush Limbaugh and Fox News, so I doubt the FCC really cares. I'm not sure the FCC has the rights to limit free speech as long as the company who owns the license doesn't care.
I believe the relevant legal authority on the question of FCC implementing content based restrictions on speech can be found in U.S. Const. Amendment 1.