It's a case of overlapping coverage. Her personal insurance company isn't disputing that the uninsured driver was responsible. They're arguing—not unreasonably—that the organizer of the event is more directly responsible for damages incurred while participating in their event (after the driver, naturally), so their insurance should cover the expense.

No one likes to be caught in the middle of something like this, but at the same time it would be irresponsible of the insurance company, toward both their investors and their other customers, to simply pay out without question when someone else should be paying.