People need to stop taking simple entertainment so seriously.
You're posting on a Star Trek
board. If people didn't take entertainment too seriously there would be no such thing.
In any event, "simple entertainment" generally = crap. It's a waste of time unless someone just needs background noise on while they drink.
No, the idea was that China was a great superpower, that China and the United States were the last bastions of human civilisation before Earth "went under".
The two most populous planets of the human civilization in "Firefly" represent the eastern and western cultures - Sihnon and Londinium. So the writer may have gotten the details wrong, but certainly understands the premise fine.