Now, Fox News and OAN and Sinclair are not, publically, actually the John Birch Society, so sure, you could say "right wingers don't think they lean right either".
Plot out a chart of US political opinion, and I more or less guarantee you that in most things, you'll find your list of media outlights absolutely "centrist", and the 3 I just named distinctly "to the right" of mainstream US political opinion.
Steve Bannon and his movement are more representative of mainstream conservatism. Even someone Tucker Carlson used to be very much like Chris Wallace. The reason why his program is so popular now is because he's shifted radically away from his establishmentarian position towards Steve Bannon's position.
Personally I don't watch Fox News because of how low to middle brow and Cathedral-like it is.
Cable TV is still a niche.