Fox News is not regulated by the FCC, it's a cable channel.
Fox also broadcasts. It does matter. As you say, Fox Broadcasting! The one thing supported the other. They pretended not to operate as a network in their early years so they wouldn't be subject to requirements of networks, but they were only just under the line. I don't know where this idea that Fox is not a broadcasting network came from except possibly for that, but it absolutely is and was one and that network supported their cable network. The two are effectively one thing, that's why they called them both Fox.