That's not remotely obvious to me. In my experience, American citizens distrust specific politicians, but they strongly trust the state apparatus. As examples, American citizens gave/give broad support to the NSA, invasions of other countries, and police/soldiers/firefighters/anyone in a uniform.
To broadly generalize, liberals seem to trust the State to be able to provide equality to people, so they might appear to "trust the State apparatus." Conservatives tend to be patriotic, so they might also appear to "trust the State apparatus." But both those groups are also trying to limit the State, just in different ways. Conservatives try to limit the social creep of the liberals. Liberals try to limit the defense spending.
I think you overestimate the "broad support" of the NSA, invasions, and uniformed men. If you've been reading the news it should be apparent that there is a huge lack of trust in the police, for example.
The cultures are entirely different, and that includes the perspective of the people towards the government. You can find many sources to support the claim that in general, the Chinese people trust the Chinese government more than the American people trust the American government. In China, the attitude toward the state is akin to the attitude of a child toward a parent. The prevailing wisdom in China is that what's good for the state is good for the people. Obviously that's not the case in America, where polls show record levels of distrust toward the government from its citizens.
These political differences stem from fundamental cultural ones, which is why I take issue with your claim that there's nothig fundamentally different about American and Chinese citizens. On the contrary, most differences are fundamental ones.