This is almost exactly mirrored on the other side of politics. See https://www.journalism.org/2020/01/24/u-s-media-polarization...
No, it's not, if you actually pay attention to the details of the study. Fox is the only source in the study in that weird middle ground, all four of the other top 5 sources Republicans rely on are on the same list for Democrats, and 3 of the other top 5 Republicans trust are on the comparable list for Democrats, and all the ones on either Democratic list that aren't on the corresponding Republican list (as well as, more obviously, those that are on the corresponding Republican lists) are significantly positive in net trust, while Fox is in that weird middle and Hannity on radio (the other one on the Republican trust list) is far in net negative territory. There are differences on the opposite sides of the spectrum, but not the kind of symmetry implied by “mirrored”.
> Given that legitimacy is exclusively a product of belief, they qualify as a 'legitimate media' source.
If we accept the first part as fact and apply the standard implied by the second, then Fox is in a hazy gray area of equally legitimate and not-legitimate, rather than clearly legitimate.
Which seems (ignoring the people who haven't heard of it or have no opinion) about right:
https://www.journalism.org/2020/01/24/media-polarization-app...