Can I be threatened with stealing a car that I paid but it is not mine?

There are several issues here. While they can "report" the car stolen if you have proof that you've been making the payments on the car (are they made directly to the lender or to them?) for the last four years law enforcement isn't going to take any action on that report. However, you do need to be concerned about getting the title to the car once you've finished paying off the payments on the car, since it sounds like you didn't have them transfer title into your name at the outset.

If they have title, they can.

Sure they can do it. The real question is - can they get away with it? Unfortunately I don't have enough info in what your message says to advise you.

It seems unlikely but make sure you have all your records in order such as any written agreement you have with this party regarding taking over the payments, and any records of monthly payments, etc. Also, it seems that if the car was truly stolen they would have reported it so back when it went missing. Finally, it is also a crime to file a false police report. Regardless, if you are truly concerned about this, you should immediately contact a criminal defense lawyer to fully discuss and evaluate this situation.