Nope. Fox News, and all news orgs are publishers, Twitter, Facebook and co are platforms. Fox News and CNN are responsible for anything published on their website. Twitter, fb, etc are not.
tl;dr: Section 230 of the Communications Decency Act of 1996 states, "No provider or user of an interactive computer service shall be treated as the publisher or speaker of any information provided by another information content provider."
The courts have upheld on multiple occasions (Pennie v. Twitter, Inc.; Fields v. Twitter, Inc.; Murphy v Twitter, Inc.) that Twitter is a provider of an interactive computer service.