What I am saying is that if this is a managed care plan (and the very large majority of employer sponsored plans are managed care plans - indemnity plans are just too darned expensive) and you went to a network physician, then there is a contract between the doctor and the insurance carrier saying how much he will accept. The insurance carrier pays that amount, and with the exception of your copay and any non-covered benefits you are off the hook.
If it is not a managed care plan (VERY unlikely if it is employer sponsored) OR if it is a managed care plan but the doctor is not part of the network, then NO contract or agreement exists between the doctor and the insurance company as to the amount they will accept (If there were, then by definition they'd be a network provider!) and thus you become responsible for the balance.
From your description, I cannot imagine that this is not a managed care plan. Basically, if there's a network of doctors, it's managed care. It also sounds as if this doctor was part of the network (your mentioning that the doctor was on the list your wife could select from sounds pretty definite to me.) If this doctor was on the network, then he has a contractual obligation to accept the amount agreed on with the insurance carrier.
I'm only guessing here, but it may be that the doctor is taking the position that since the other party to the contract (the insurance carrier) is no longer viable, the contract is void and he is free to balance bill you. If that's the case, you may need legal assistance to make the point that since the contract was in effect at the time of the surgery, the terms of the contract still hold.
All of this assumes that before going bankrupt, the insurance carrier had already paid an amount equal to the negotiated rate. If that is NOT the case, then it MAY be, depending on how the bankrupcy ( a subject I am NOT qualified to discuss) was handled, that there is a balance owed by you.