Out-of-network ER balance bill for $6,200 after a 90 minute visit at a hospital that says it's in-network with BCBS PPO. Surprise Billing Act should cover this right?

Looking for a sanity check before i pick a fight with BCBS. My wife had a kidney stone episode in February, went to the closest ER which is the hospital our PCP refers everyone to and is listed as in-network on the BCBS provider directory. She was triaged, given a CT, given IV fluids and pain meds, observed for about 90 minutes, and discharged. Total visit was barely an afternoon.

The hospital itself billed in-network and BCBS paid that part. The problem is the ER physician group that staffs the hospital is a separate corporate entity and they billed out-of-network. Their bill came in at $4,400 and BCBS paid $1,800 toward it claiming the out-of-network allowed amount is $1,800 and the rest is patient responsibility. The physician group sent us a balance bill for $2,600. Add the imaging radiologist who read the CT, who is also a separate out-of-network entity, and we are looking at another bill for $1,400. Pharmacy and lab were in-network and not at issue. Total surprise balance bills come to about $6,200 between the two.

My understanding is the federal No Surprises Act, which has been in effect since January 2022, specifically prohibits out-of-network ER physicians and radiologists at in-network facilities from balance billing the patient beyond the in-network cost-sharing amount. We never signed any kind of notice or consent. We did not pick the ER doctor or the radiologist, they were assigned by the hospital. This seems like a textbook violation to me.

Has anyone successfully fought a balance bill like this under the NSA? Do i call the physician group first, BCBS first, or just go straight to the CMS complaint portal? The bills are not yet in collections but the physician group already sent a second notice with a "pay within 30 days or interest accrues" warning. I want to handle this correctly the first time.