They get this source of funding because that is how they were created and entities that were created through a different mechanism (for instance: to become the mouthpiece for a political stream or for commercial reasons) are a different kind of animal.

The government allocates funds to many things that it may consider useful, such as health care, infrastructure and education. This does not necessarily imply that the government does this to create a mechanism of influence, as opposed to their counterparts in countries that are run as dictatorships. Naming the NPR in the same breath as the Chinese, Russian, Iranian and North Korean state media is mistaken at best and maliciously dishonest at worst. Knowing what I know about Musk it is a fair bet we're looking at the latter.

It should be under the same label as BBC, just govt-funded. Up to you what you think of that. State-affiliated means definite editorial control. Syria etc call those outlets education too.

And I'm pretty sure they'd have been fine with that, however, the BBC label reads 'Publicly funded media', not 'Government funded'.

"Publicly-funded" is fine too.