It seems to be a hopeless situation which is very common. I have two suggestions, one is to negotiate with the anesthesiologist's office for a payment term or reduced payment amount; the other is to verify with your insurance policy terms to see whether there is a RAPS or ARPS provision to treat the out of network provider as the in the network provider. The reference below is from a local Pathology Association in Iowa. It makes some sense. The citation is presented in the question and answer format.
Also, usually, prior to any scheduled surgery, the hospital or the specialist's office will verify our insurance plan to check how much the cost will be and what payments will be paid by our insurance plan and ourselves. Bring this issue to that person or unit in the hospital which should have verified the information for the patient and complain about it. This is where you ask and should have known "how were we to know." I would start with the hospital.
Another way to process this is to call your state's insurance regulatory board and file a consumer complaint and see how far this can carry for you. Start with this website. https://online.doi.sc.gov/Eng/Public/Consumer/healthinfoSCconsumer.aspx
Please read on the citation below and feel free to follow up.
Fiona Chen, MPA, Ph.D., CPA, ABV, CFF, CITP
My insurance applied these charges to my deductible. My deductible has been met, why did my insurance company process the claim this way?
You may have two separate deductibles; one for in-network claims processing and another for out-of network claims processing. Please contact your insurance plan at the telephone number provided on the back of your insurance card to inquire about why they processed your claim in this manner.
My insurance company will not pay for a certain portion of charges that they call UCR (Usual, Customary and Reasonable). Am I responsible for the UCR amount due on my account?
The UCR is the amount your insurance carrier considers the Usual and Customary allowance for this procedure. UCR adjustments are not allowed unless we have a signed contract with the insurance carrier. Some policies have RAPS provisions. This is an acronym for Radiology, Anesthesia, Pathology and Surgical procedures. These are also referred to as ARPS (Anesthesia, Radiology, Pathology and Surgical). You may want to check with your insurance carrier to see whether your policy has a RAPS provision.
Many times there are RAPS for facility only; which means that if you were seen at a hospital or Skilled Nursing Facility setting; such as a care center, RAPS may apply and your claim could be covered at in-network levels. Other plans have RAPS if you were seen by an in-network referring physician. If you were seen by a participating provider then anything submitted to Radiology, Pathology, Anesthesia and Surgery for further testing is covered at in-network levels if you have this RAPS provision on your policy. It is your responsibility to check with your insurance plan and verify that any referrals and prior authorizations are in place before services are provided.