And this happened to me. Got a call from a collection agency claiming I owed them money a year after the birth. I called the hospital and got a written confirmation that they had no record of an unpaid or even late bill. I called my insurance and confirmed they had never received a bill for the amount claimed. Upon getting details from the debt collector (later than required by law), I saw a doctor's name. So I went to the hospital, and they had no record of a doctor by that name ever working for them.
The bill turned out to be legitimate, in that the doctor was a "traveling anesthesiologist" and was never an employee of the hospital. And they billed separately, and were never given my insurance information. The whole case ended up relying on my wife's signature on a long legal form that she signed while she was dilated to an 8. All the contact information (address, phone, company name) on the documentation led to people who could not confirm any details on the bill. The hospital told me that they have had a lot of reports of doctors who do their own billing not sending bills for months because they're not very organized.
Eventually the anesthesiologist billed it to my insurance correctly and I paid 10% of it. I later found out I could sue the debt collector for not providing details fast enough, but the statute of limitations on their violation had expired.