The insulating properties of air is about 1 inch of gap is around 5000 volts of insulation Now that is without an arc. So for your dump truck and spark gap he was likely less than 3 inches from the wire at the moment the arc struck. Next the nail in the tire would not reduce the trucks dielectric very much at all. since the frame is isolated by the tire at the axle. I don't find the truck drivers claim to be credible at all. unless their was a chain or something in contact with the ground and a space less than 3 inches from the box to the OH wire both occurred at the same time it would not likely have jumped across at all. A load break switch at that voltage uses simple arc chutes and air to break the flow and the blades only open a foot or so.
Once conducting the insulation value of air is a lot lower and might have been able to pull an arc for a couple of feet max. Limits of approach for that voltage is 10 feet. At that distance there should almost be no chance of jumping across that gap. In Cancun the plasterers I watched working on the exterior of a retail/condo was easily within 5 feet and no crispy plasterers in the area.