Are you really comparing state-owned agencies to independent media companies?
That screams more "state" than "public" control.
Wikipedia portrays it differently, I wonder why.
No, not really: https://www.bbc.com/aboutthebbc/governance/licencefee.
They're not state-owned but they are certainly not independent. All mainstream media is tightly bound to a political party or another. Fox and MSNBC are mirrors of misinformation.