The U.K. equivalent is GB News. Its reality is worse than your hypothetical. (-:
But the level of Foxness that I was alluding to was not that of GB News, but rather more that of Reach PLC; which isn't Murdoch-owned, but which runs a whole network of purportedly regional news outlets which turn out to be just localized skins applied to a big syndicated empire, and which BBC News often does better than locally.
Yeah in the US system thanks to some old competition requirements the Affiliate Network gets most of the name recognition and provides most of the prime time entertainment content (a few other content blocks), but the stations under that network have their own owners that can be more or less damaging, especially in news content, and more or less "invisible" in that maybe you only see their name in the fine print at the end of credits or copyright statements.
One other notorious example is Sinclair Broadcasting [1]. Sinclair-owned stations include all of the major Affiliate Networks in the US and some of the minor ones, but are known for how much they farm politically-biased news content across their platforms, including trying to pass off editorial content as news content.
(ETA: Which is to say that yeah a FOX affiliate gets entertainment programming from what is left of Rupert Murdoch's empire, but could be getting news content from all sorts of places from home-grown proper local journalism to content farms from their real owners.)
But the level of Foxness that I was alluding to was not that of GB News, but rather more that of Reach PLC; which isn't Murdoch-owned, but which runs a whole network of purportedly regional news outlets which turn out to be just localized skins applied to a big syndicated empire, and which BBC News often does better than locally.