> about how Claude or even Codex have refused to perform some normal program development tasks

> a lot of reports that the US LLMs refuse to answer questions

I think the specific ask is for a case where the LLM is trained to lie about something. What you've come up with are cases where it refuses to do something, possibly for legal reasons but maybe not (you can come up with plausible non-legal reasons why a company training an LLM might want it to refuse to give you instructions on making a bomb, even if instructions on making a bomb are protected First Amendment speech).

An LLM that responds with "I'm sorry, due to legal requirements placed on my creators, I'm unable to answer questions about events at Tiananmen square in 1989." strikes me as much less problematic than one that pretends there is no relevant or reliable information that exists, or explicitly supports a regime narrative. But I'm also of the opinion that an LLM refusing to help you build a fertilizer bomb is much more reasonable than one that suppresses information of a political nature. I can't think of a case where information that reflects the broad consensus of experts is suppressed by US based LLMs for political reasons.