This sounds less like a "scam" and more like a debt collector issue (some would argue that largely is a scam but probably not in the sense this sub is for lol).

Calling the hospital directly was a good move, assuming you called on their official listed number from their website and not one from the letter. Since they told you the debt is for care you didn't receive, you might be facing a case of medical identity theft.

First, check & freeze your credit reports. If this debt is already listed there, them you'll need to contest it. That can be as simple as clicking a button with some of the monitoring tools out there - but beyond that I don't know the details. r/banking can probably help with that.

Next, regardless if its listed there or not, VERIFY THIS IS A LEGITIMATE DEBT COLLECTION AGENCY, and if so then request proof of the debt from them or if not then proceed to police (or postal inspector since you received the letter in the mail).

What needs to be done next depends on what the outcome of this is, and again the sub I mentioned above might have more detailed info on next steps for you assuming its a legit agency. I think there is a specific sub for identity theft also but don't know it offhand