While true, you neglect the fact that US corporations have some autonomy from the government. I doubt that any of the current American AI corporations get regular dossiers of desirable responses to sensitive political topics from Washington and implement them. That would be a reason for a major lawsuit and a major scandal.
In China, the image of the country and the preferred narrative is under much tighter control of the government and local AI shops won't have any autonomy in this regard at all. Either obey or get shut down.
BTW What you mean by "weaponizing human rights", exactly? I am curious. If anything, I would say that the US foreign policy didn't promote human rights sufficiently, especially in Latin America, where the "bastard, but our bastard" attitude was typical.
OTOH in Europe, US human rights policy was probably relevant in saving some dissenters in the former Eastern Bloc from torture or execution.