I am not in debt to my old leasing agency after all!
I called the accounts manager who sent me the letter and told them my story. I also called the leasing agent who offered me the deal (the amount I thought I needed to pay and had paid). A few days later, the leasing agent got back to me. He was quite apologetic and said this never should have happened. He had a note in my file that we had made this agreement, and somehow, it never got to the accounts team.
The next day, I received an official letter from the accounts manager saying that I was paid in full.
$7500, back in my pocket.
But lesson learned, boys and girls. GET IT IN WRITING!