Am I legally responsible for this debt???

A little over 3 years ago, I had some wisdom teeth pulled by my dentist, in Atlanta, GA. The agreement was that I pay 20% of the bill, and he would charge my insurance company for the remainder 80%. It was verified before surgery that the insurance company would cover the claim. However, the dentist failed to file a claim within 6 months of the surgery, and the insurance company refused the claim stating that was the reason. Now I am getting calls from a collection agency. Am I legally responsible for this debt? To my knowledge, I did not agree to be responsible if the insurance company refused the claim. Isn't the dentist negligent by not filing the claim on time? Thank you to anyone that responds!