That's a long story available in numerous books. I've come across the details in a book about Eisner's Disney years, WDW, and Disney in general. Long story short, Disney was going to contract out ALL hotels from construction to operation (after the building of the Contemporary & Poly) as they didn't want to be in the hotel business. After having cut a deal, they reviewed the plans, observed the contracted firm was basically building unattractive boxes (the norm for hotels back then) and then changed their minds realizing that Imagineering could do a far superior job and bring more magic and uniqueness to resorts. The way out of the contract was to allow for the construction of 2 resorts to be owned by said company on WDW property, though Disney forced the more extravagant design of them so they went art-deco (a popular style in Florida at the time) and pushed the design limits to make them more attractive.
Anyone can correct me if I'm wrong, but that's the Reader's Digest version I've assembled in my head from the numerous readings.
You have the correct general idea, just a couple of corrections...
The Hotel Plaza Project was pushed by Ron Miller to rapidly expand WDW's hotel room capacity, faster than WED could do it alone (and with money Disney didn't have), not because Disney was interested in contracting out hotels to separate management companies. (Although this did come up at a different time with Marriott being the biggest player, save that story for another time.)
When Michael Eisner came to Disney (a big fan of good architecture), he saw Hotel Plaza's bland buildings and was shocked that Ron had already signed the contract to allow two more hotels built in the same manner. He immediately went to Tishman Construction (this is the company you are thinking of) and demanded that work not start on any future Hotel Plaza Hotels until Michael had a major architect work up some new designs for the buildings. Tishman was angry that this would hurt their profits by stalling construction by 2 years, and they demanded something in return.
Eventually, a compromise was made to allow the remaining two hotels to be centrally located on property (still owned by Disney, mind you) and be integrated into Disney's property as much as possible. (With transportation, watercraft connections, etc.) That led to the design and construction of the Walt Disney World Swan and Dolphin. And that is how you have two hotels on property owned by Disney, connected with Disney Transportation and Disney's reservation system, yet the buildings are owned by Tishman, and managed by Starwood.
So, blame Michael for the giant hotels there, or applaud Michael for putting a stop to more ugly hotels on Hotel Plaza. Either way, this is a Michael story. Personally, I just blame Ron Miller for just not going with WED to do the hotels in the first place at a slower pace until they had the money, but that's just me.