They are thinking that they are not liable since they didn't operate the track.
The track is operated by Petty Holdings, which has other Exotic Driving Experience attractions at speedways in Atlanta, Daytona Beach, New Jersey, Kansas, New Hampshire and Texas.
Who sponsored it?
I think if the company (Disney) took someone's money in exchange for a service, and something bad happened during this service, they won't be able to wiggle out all that easily. The company would have to demonstrate that they performed all the reasonable and expected steps to ensure safety of their customers. It would be trivial for the opponent to show that giving random people control over powerful cars with unique control characteristics simply cannot end well. It does not matter who operated the track, as long as Disney knew about it and allowed its operation.
Thank you