If you really believe that you are not liable for the charges, don't pay the bill, OP. If you pay the bill, you are essentially agreeing that you are liable. You'll then have to explain to a judge why you paid the bill when you did not believe that you were liable.
That said, you might actually be liable. You doctor is not in-network. Thus, his office is not bound by your insurance company's procedures. It might well have been your responsibility to ensure that the colonoscopy was pre-certified. Check the handbook that your insurance company provided during the open enrollment period.
In your position, I would try hard to get the claim paid.
First, ask the doctor's office to call the pre-certification line and attempt to have the procedure "pre-certified" retroactively.
Second, appeal directly to the insurance company. Try to speak with the pre-certification department to find our what the criteria are for pre-certifying your procedure. Then write to them and ask them to review your claim. Explain how you would have met their pre-certification criteria had the doctor's office called. Included copies of your medical records.
Third, write to OPM and them to intercede one your behalf. Explain that you would have met the pre-certification requirements, but your out-of-network doctor forgot to call.