Hospital did not submit claim to insurance until after the filing limit. Am I responsible?

Hello, a year and a half ago i had major surgery. Three months ago i received a call from the hospital looking for payment on an outstanding bill. I informed the caller that all hospital bills were paid in full. He looked through the paper work and realized that the hospital never sent me a bill for the physicians – I had no idea that the physician’s fees were not included in the overall hospital bill. The insurance will not pay two of the physicians bills as the claims were filed ‘beyond the plan’s filing limit’. My question is am I responsible for the charges in full do to the hospitals failure to file a claim?