It might seem so til you consider how an LLM is trained.

An indirect illustration: I can attest that Deepseek has very good 19th German, and knowledge of German 19th c literature, science and historical scholarship. No one in China could control the training that led to this. The German training sources were well aware of the exact nature of eg American slavery, so they are in the weights.

State control operates in the outer layers not the llm itself.

People can and will use LLMs to curate the training data for the next generation. I expect they already do.