Somebody correct me if I am wrong, but I think the land is owned by Disney, and leased to the Starwood Group, who own the Swan and Dolphin Resorts.
Personally, while staying at both resorts, I didn't lose any of the so called 'disney magic' by not staying at a "disney resort." The CM's there are all fantastic, housekeeping is impeccable, plenty of theming and beautiful landscaping, not to mention boat transportation to MGM and Epcot! Or, you are close enough to both that you can even walk.
I'm sold on the Dolphin, it is one of my most favorite places on earth!