My understanding is that if you're participating or in their network, you agree to take the allowed amount and write off the balance.
I have run across many more auto and worker's comp policies who are now connected to other review companies (CorVel is one, United HealthCare is another, Blue Cross comes up a lot for us). So your provider may not even realize they are "in network". Research should be done to see how it's all connected for your office.
Your office should have all their facts in order before the sic the collection agency on the patient.
Also, when it's an auto accident, different rules apply. If you're truly non-network, contact the insurance company and try to get the balance paid. If they won't, and you are non-network, you can always have the patient sign a lien against the final settlement.