Can dentist send me bills half a year later claiming my insurance didn't cover all costs?

I had some dental work done and paid off all balances right at the dentist office. The staement showed a balance of $0. I just received a bill from the dentist, six month after that work was done, claiming that I owe them money, and that the bill is past due. Even though this is the first letter I received from them! I moved out of state 2 months ago and also changed insurance since I have a new employer. Can they still come after me?
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Why would you NOT owe the money? You have your original bill or EOB, I hope, and you can simply look at the amount charged and compare it to the amount paid. Do the math and that's what you owe. IF, on the other hand, you were participating in an HMO type thing where the dentist is required to accept only the insurance payment as payment in full (and you would know this if you read your benefit booklet or called your insurance carrier), then you should not owe anything outside of any deductible or prescribed co-pay. Of course, is this is the first bill they sent you, it's kind of tacky to say that it's past due already. Unless they sent 2 or 3 bills to your old address and they were not forwarded and it took them until now to track you down...
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