Have you verified that the dentist's office actually received the payment from the insurance company? It sounds like they may not have, or if they did perhaps they misapplied the payment.

I would start by asking them this. If they confirm it, the matter should be settled (less any deductible of course). If they don't have it, then it's time to call your insurer and see if they have proof of payment.

In any case, you certainly cannot be required to pay a bill already paid by your insurance. So it's just a matter of figuring out where the mistake was made and getting it corrected.