Pure speculation on my part, but I could not imagine Disney not self insuring itself for such a small amount of damages. I think they have reinsurance for some catastrophic losses but a small fire is a drop in the bucket for them.
I swear I saw a thing on TV about insurance companies requiring testing of wind loads on the EPCOT ball (sorry I couldn't spell geodesic sphere ;)) but that it was someone like Lloyd's providing reinsurance, but I could just be full of it.