The progressive advocacy organization MoveOn just charged Fox News with refusing to run one of its television commercials.  The commercial, entitled "Lied to You," accuses Fox News of lying to its viewers about the 2020 election.  In a statement, MoveOn explained that the commercial, "quotes recently released e-mails and text messages from Fox News executives and hosts showing they intentionally presented false allegations about election fraud, during reporting on the 2020 presidential election results, to keep ratings and profits up."  (According to media reports, Fox says that it disputes these allegations)

It's no surprise that Fox refused to run the commercial -- and, if I had to guess, I imagine that MoveOn didn't really think that Fox would accept it.  The truth is, it's highly unlikely that any network would accept advertising that criticizes the network.  

Networks and other media organizations generally have departments that are responsible for pre-clearing advertising that runs on their platforms.  Many of them have also published advertising guidelines that define the types of advertising they will and will not accept.  (Here are the Fox Advertising Guidelines, for example.)  And, for the most part, media organizations don't have any obligation to accept advertisements that they don't want to accept, and they reject ads for a wide variety of reasons.  

Sometimes, media organizations reject ads -- or request revisions to proposed advertising -- for relatively non-controversial reasons. For example, a commercial might be rejected because it's making false claims, because the disclaimers in the commercial aren't readable, or because the commercial encourages kids to engage to unsafe behavior.  Commercials and other ads might also get rejected because the network or other media organization has just decided that the advertising topic is not appropriate for its platform -- such as Hallmark's rejection of a commercial that shows brides kissing (which it later apologized for), ABC's rejection of a commercial about postpartum recovery, CBS's rejection of a commercial that depicts a commercial depicting menstruating men, and CNN's rejection of certain commercials from the Trump campaign, to name a few. 

Although I haven't seen any reports yet about what Fox has said (if anything) about its reasons for the rejection of the MoveOn commercial, it's pretty clear from its Advertising Guidelines that this is not the type of commercial that Fox would accept.  As Fox's guidelines explain, the network "reserves its right to decline or restrict advertisements that do not meet its standards, are contrary to the expectations of its audience or disparage our company, people or partners, or members of our audience."