The presence of insitutional bias in media is well established. No one has every really put the lie to Herman and Chomsky's Manufacturing Consent.
I think the concern specifically with Fox News is that any actual reportage is a side-effect, a fringe benefit.
Let's look at a parallel situation. There is a free daily newspaper in Israel called Israel Hayom. The paper was started by Las Vegas Sands owner Sheldon Adelson with the sole purpose of getting Netanyahu elected as PM and advancing a conservative political agenda in that country. Adelson invested $180M in the project, and the newspaper thrived.
Does Israel Hayom report news? Probably, but again, that's not what Adelson cared about when he started the paper, and it's not what his editors or reporters are concerned with when they produce it. They mold the information to fit the stated agenda, and the stated agenda is overtly influencing the opinions and votes of a democratic nation.
I think that's the central concern behind this post.
Yes, per Chomsky, every journalist has to watch what he or she writes about institutional players because if they get mad then official sources of information dry up. That does create an implicit bias in reporting, i.e. piss off the White House and your paper doesn't get White House press releases any more, so you don't piss off the White House if you can help it.
However, not every journalist is writing from a predetermined set of political ideologies, not every editorial represents a party line, and not every commentator is belligerently prejudiced against any viewpoint which doesn't fit a checklist provided by his network.
Fox News and its backers want to change the way we think about the world in a very specific way, and every aspect of programming is designed with that in mind. That isn't news, it's manipulation. That isn't commentary, it's propaganda.