Loan resurfaced

We had paid off our auto loan, even got the title in our hands. 6 months later, last week they said that there was a transaction issue and that we still owe them more than 6K. For 6 months our account said $0 balance but now it shows we have $6400 balance and it is 186 days overdue. Thek wrote a rude email today threatening to send it to collections. We both have very good credit and are planning to buy a house and dont want to be hurt by this. At the same time we dont want to pay what we dont owe.