This is one of the times where I think I already know the answer, but a second-opinion wouldn't hurt.
I had someone at a company contact me about doing a design for them. The agreement was simple; they would pay for the time and effort to create the piece and buy the rights to use it for a single purpose. There were no contracts signed, simply a few e-mails back and forth agreeing to those terms.
I just found out that they, in short, are no longer interested but may want it in the future. I've also never gotten paid for it.
So here's my question: That means I can use it how I see fit now, right?