I'm anxious to see if "inciting others to imminent lawless action" gets tested after everything that happened on 1/6. There have been bar exam questions in the past that have had facts patterns extremely close to the speeches on 1/6 that didn't confer First Amendment protections on the speaker.
As far as what may have spooked the Fox News lawyers, the freedom of the press allows Fox News and the like to publish matters of public concern. It is very broad, as even the Pentagon Papers were determined to be protected, and that contained a few defense secrets. However, I would think that ever since Fox News issued that legal defense that Tucker Carlson is an entertainment program and not a news program (cite: https://www.npr.org/2020/09/29/917747123/you-literally-cant-believe-the-facts-tucker-carlson-tells-you-so-say-fox-s-lawye ), then I would think that Tucker, Hannity, and the like could actually be classified as commercial speech as it is speech on the behalf of a company with the intent to earn profit. Commercial speech is not afforded First Amendment protections if it is false, misleading, or deceptive.
And even if it isn't commercial speech, a couple of well-placed subpoenas could reveal that Fox News is knowingly falsifying the news that they put out there. Possibly even with malice. With Murdoch's deep pockets, Fox News will always have a "don't like it? Sue me" approach to civil claims regarding their content, but the US government has deeper pockets. If Fox News is pulling back, it's because their lawyers are worried that they are risking the loss of First Amendment protections, not civil suits. And Tucker knows that Fox News will gladly push Tucker and whoever else out to sea and let the sharks have them just to spare Fox News even one red cent.