Even so, it's rather common for doctors to not be albe to diagonise correctly. It's a guessing game for them too. I don't know so much about US but it's a real problem in large parts of the world. As the comment stated, I would take anything a doctor says with a pinch of salt. Particularly so when the problem is not obvious.
This is really not that far off from the argument that "well, people make mistakes a lot, too, so really, LLMs are just like people, and they're probably conscious too!"
Yes, doctors make mistakes. Yes, some doctors make a lot of mistakes. Yes, some patients get misdiagnosed a bunch (because they have something unusual, or because they are a member of a group—like women, people of color, overweight people, or some combination—that American doctors have a tendency to disbelieve).
None of that means that it's a good idea to replace those human doctors with LLMs that can make up brand-new diseases that don't exist occasionally.