It matters because for medical questions, you [are supposed to] go to a medical professional, and those very much cares about and make that distinction.
Which is exactly the problem here; it "used to be" that reasonable people would disbelieve random things they find on the internet at least to some degree. "Media literacy". LLMs don't seem to have that capability, and a good number of people are using LLMs in blissful ignorance of that fact. They very confidently exclaim things that make them sound like experts in the field at question.
Would it have made a difference for the AI data center heat island thing you're quoting? maybe not. But for medical matters? Most people wouldn't even have caught wind of this odd fake disease. LLMs just amplify it and serve it to everyone.
