Both states say the former though, who are you kidding? You can argue over which one is being more truthful but you're literally just deciding to think critically only about the US's justification and not China's.

I think it's also important to note that the majority of people sent through the re-education system just ended up with vocational training and a job that paid significantly more than what they had before. That alone is probably the biggest driver of de-radicalization. Who would think that improving people's material conditions would lead to them being less inclined to join a radical separatist organization?