Accidents and timely filing-hospital didn't file

I was in a car accident 7/3/19, not at fault, taken to a not-for-profit hospital via ambulance, where they took many scans, etc before releasing me. We did provide insurance info to a case worker at a later date. At that same time, we gave the attorney info, as this was now part of a pi case. Much later, we found out no claims were never filed by the hospital because they "never received the insurance information", yet they have the attorney's info sent at the same time... Now, of course, they want the bill paid in full. Do we have any recourse to make them file a claim, forcing them to a write off, even though timely filing has expired?