Will a doctor's office write off an amount that the insurance deems over the maximum billable amount that they allow?

Yes, if they are on the provider list. Yes ONLY IF they are obligated to do so under a network agreement. If your insurance company determines that procedure X should not exceed $100 and that is the maximum they will pay one of two things can happen. If the doctor is in the insurance companies network then they are likely obligated to accept that maximum amount and write off the difference. However, if the doctor has no such agreement they will bill you for the difference over and above the insurance reimbursement and you are obligated to pay it. That said, try to negotiate because there may be some room for compromise.