US free speech law, in practice, does usually protect liars. That's generally a good thing, because there's a lot of grey area. But I think it's terrible if we, as outside observers, get caught up focusing on the legal wranglings and who we like and dislike, before seriously asking the question of what's true.
I don't have access to much in the way of data about Twitter. My own feed is healthy, but it's mostly composed of people I know who I've chosen carefully, so people who follow more indiscriminately might have a different experience. But I did check out the CCDH's recent blog posts, randomly clicked on one about LLMs, and it seemed pretty dishonest to me (they prompted it with jailbreaking prompts, then in the summary made it sound like it would say offensive things without jailbreaking.)