Yes, there typically has to be reciprocity; this is what closed off the world's media throughout the entire duration of the Cold War, and is the paradigm under which China (and Russia to an extent) still operate. It's why RFERL, originally a pro-American propaganda radio broadcast targeted at Eastern Bloc and communist countries, was created, and why you could go to jail for listening to it in the USSR. Actually, currently, you still can (in Russia under their wartime laws).

It wasn't and still isn't legal to run an unregulated foreign-owned news bureau in basically any country. Social media is enmeshed with current events / news so it falls under like jurisdiction.

"Schizo" applies here as there is a definite schism between countries in the world and always has been. Try operating a HAM radio around Florida/Cuba and you'll find the southern neighbor has jammed (I believe) most radio news coming from the US.

In general, reciprocity works well across a broad range of international relations, (visas, tariffs, mutual defence/non-aggression/..., and otherwise).

As an idea, it's not "too dumb to believe."

Indeed, it's one of the places the US' draconian visa policies often come back to bite it. If you're travelling to any developing country with reciprocity on a US passport, you can expect to be treated horribly.