So what? People are wrong all the time. What happens when people are wrong? Things go wrong. What happens then? People learn that the way they got their information wasn't robust enough and they'll adapt to be more careful in the future.
This is the way it has always worked. But people are "worried" about LLMs... Because they're new. Don't worry, it's just another tool in the box, people are perfectly capable of being wrong without LLMs.