Unless they are advertised as medical practitioners, I don't see how they could possibly be liable for bad medical advice. You can't sue your friend or dad for bad medical advice. Maybe you can if they claim themselves to be a licensed medical practitioner you'd have a shot at a successful lawsuit.
You don’t have to claim you are a licensed medical professional to be sued for medical advice that harms someone. You just need to present your advice in a way that a reasonable person would assume that you have some kind of medical expertise.
Based on the confident manner with which all LLMs present their answers and based on the fact that people are clearly using LLMs for their medical expertise, I think it would be pretty easy to go after one for giving medical advice that caused actual damages.
My guess is that the end result is that companies are going to tune their models to default to telling people to go to the ER.