Either the doc billed first or the doc's office billed with the wrong code. Call them, ask them to re-bill with the "emergency care" type of code.
Ask the insurance people to see who billed when. If the doc billed first, ask if they can make sure their system understands that this was an emergency situation. I dealt with a ambulance bill (in my city we pay for them, they aren't covered by taxes) for almost a year before an insurance CS person noticed that their system "thought" that the ambulance ride was for a non-emergent situation, and had paid out on that basis. Once she switched it around, I actually got a check back. (and then the ambulance company decided to honor the discount they initially said they would give me then took away a week later so I was done with them, too!)
I had a situation where I was told "emergency! emergency!" at an in-network hospital, by an MD that was on-call and just "given" to me, and it turned out he was out of network. He billed as non-emergent, and REFUSED to change it, and I don't know why. I paid for years on that thing, so de-moralized that I never tried harder. I ought to contact them again AND contact the insurance commissioner, because you can't just scream "emergency" and then not bill as such, especially when you KNOW you aren't a part of that hospital's network....
Good luck!