The only way that would work is if they were physically in contact with the van when they jumped. Sayid, Hurley, Jin or Miles could all have initially been in the van. Remember that when Sawyer was holding John on a rope in the well and they flashed? Sawyer was still holding part of the rope. This is the only explanation for the van. Otherwise, it would not have been there or would have been rotted out.
As for the supplies, I would imagine that all Dharma vans would carry this type of stuff in the jungle for emergencies.
to the death