In-network doctor but out-of-network hospital result in $270,000 on EOB

The medical insurance I have is Emblemhealth and Anthem BCBS. It seems that Anthem BCBS is related to the hospital. I had an Ankle Arthrocentesis in February and the doctor was an in-network doctor. I received an EOB from Anthem BCBS two days ago, which said that all claims were denied because the hospital is out-of-network, and I needed to pay almost $270,000. I contacted my doctor immediately and he stated that it was an EOB not a bill and I wouldn't pay that much when the bill comes so do not worry about it.

How could I not worry? $270,000 is a number that is enough to ruin my life, although it says "Don't worry, this is not a bill" on the EOB. As far as I know (I didn't learn much about medical insurance before this), the bill needs to match the EOB, so this is my biggest headache at the moment.

I searched a lot of cases on the Internet, but non of them matched my situation. I don’t know if this is a “surprise bill” because it was a procedure scheduled in advance, although my doctor told me before the procedure that my insurance would cover everything. The hospital staff did not inform me before the procedure that this facility is out-of-network, and I confirmed to the hospital that I did not sign any "Out-of-network" form.

Before receiving the EOB, I received a letter from the hospital. I didn't quite understand what the letter was saying. The content of the letter is as follows:

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Insurance Co: HORIZON BLUE CROSS BLUE SHIELD

We have billed your insurance company for the procedure performed at our facility on above mentioned date. Since this facility is out of network your insurance company will send the payment that is due to us directly to and payable to you or the policy holder if you are not the member.