That assumes people mistrust LLM output, which is a perspective inside the HN bubble.
Outside, almost everyone I know - including highly educated people - takes even Google's search LLM output as fact, without a second thought, and even regarding serious issues (e.g., medical problems). Nobody raises a doubt or an eyebrow. A recent article says members of US Congress use it extensively for serious work. Lawyers use it to file cases. Doctors use it to summarize essential medical information. I even hear that software developers use it to create high-risk, high-value code.
In the public people think computers are superior to humans - more authoritative, objective, perfectly logical and error-proof. SV pushes that narrative, for example saying computer-driven cars are safer because computers don't have human flaws (that old sales technique - compare only the competition's unique flaws and don't mention your own; computers have their own flaws that humans lack). And of course, that one is popular on HN.
(IMHO the way to educate the public is to spread the narrative that every computer is created (designed, programmed) by normal, flawed, biased, etc. humans, and controlled by other flawed humans for their own agenda. And that computers have their own flaws.)
The Elon buttlicker types praise llms as the new knowledge gods.
The general public distrusts them cuz they know that they're coming for their jobs. But they will use them out of convenience
The fact that you conflate LLMs and AI means you’re unqualified to be part of the discussion