There's nothing anyone can do about state-level espionage anywhere, using any cloud-hosted service. That being said, there is a very big difference between the legal situation in the United States vs. China. Chinese internet companies are required to have CPC interaction and since the rule of law does not strictly exist in China, the state can compel surveillance cooperation regardless of what might be written down. If a three-letter agency is compelling Anthropic to open up its queries for inspection, that kind of surveillance would be authorized by law and if Anthropic violated the law in cooperating, they would suffer the consequences in civil court. Maybe not immediately, but at least the possibility exists.

In China, there's no recourse at all. Surveillance must be presumed.

There are legal protections, and those companies have more to lose by breaking those laws than following them. Same probably not true for Chinese companies.