Surprise bill from dentist for amount insurance did not pay. Insurance says I should owe nothing

I went to a new dentist for a regular yearly cleaning last year. They are in-network for my insurance and they billed my insurance. My insurance paid them the allowed amounts and tells me I should owe the dentist nothing else. However last month I got a bill from the dentist for the remainder. I called my insurance and they told me that I should not owe anything and sent me some paperwork to give the dentist as proof. Neither myself or the insurance person were able to talk to someone at the dentist office because their billing phone number goes to voice mail and their voice mail box is full. We both called multiple times at different times of day. Now it’s past the due date on the bill I got and I don’t want them to send me to collections for something I don’t owe. I am going to go into the dentist office to try and catch them in person but want to make sure there isn’t some sneaky rule I don’t know about that says they can bill me even though my insurance says they can’t. Is this right? Thanks!