Emergency Room Run by Staffing Company

Had to go to the ER at the local hospital. It's now run by one of those ER staffing companies, which I understand is the norm now. I have great large-group insurance coverage and you would think the ER staffing company would be listed in the provider directory, but it's not, just the hospital is.

Should I anticipate any problems with out-of-network billing. I find it hard to believe that would be a glitch, but figured someone here might have some insight. Thanks!