They are both independent non-profits which rely on a mix of private and public funds.

Not sure through what mechanism you think they are directly controlled.

The state-controlled CPB exerts significant influence via funding and the FCC via regulatory reach. This isn't theoretical. Whether that's "direct" control or not is in the eye of the beholder, but people have accused media in other countries of being not independent under similar circumstances.

Personally I think anyone can live in their own fiction as long as they are not hurting anyone else, but to consider a strategic resource like the media as being truly independent in any country is naive. You're literally missing an entire world if you do not look outside your home country.

No, you’re thinking of VOA and stuff that used to be under erstwhile Broadcasting Board of Governors