The US has no legal authority within China, or any other country, which is why the State Dept website says "You must follow the local laws of the country you vi

The US has no legal authority within China, or any other country, which is why the State Dept website says "You must follow the local laws of the country you visit". It's pretty much a negotiation. The State Dept can try back channels if they think you've been unfairly denied an exit visa, but other than than, there is nothing they can do.