However, ownership of the show itself is a bit more complicated. While Opryland USA produced it, TNN (later renamed Spike TV and now Paramount Network) aired the show and likely held the distribution rights.
Ownership of the show's rights may have changed hands over the years through various mergers, acquisitions, and licensing agreements. It's difficult to say definitively who owns the rights today.
You can try contacting Paramount Network or doing research into the history of Opryland USA and TNN to find more information.