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.
Even if Disney had liability, they would have an indemnity clause that would require the vendor to indemnify Disney for any and all liability resultant from the vendor’s operation.
So they sue Disney and Disney just tells the vendor to pay their attorney fees and any award.