I saw the car buried and now I've seen it dug back up. It was built to withstand a nuclear bomb because fear of nuclear war was on everyone's mind in 1957, but it was never intended to be anything other than a vault for the car. At the time Tulsa's largest employer was Douglas Aircraft, building Boeing B-47 bombers for the Strategic Air Command, so Tulsa folks considered the town a prime target for a nuke attack.
The car was buried in a spirit of celebration of Oklahoma's 50th anniversary of statehood, but I think in many people's minds, they thought it might be the only thing that survived the unavoidable nuclear attack. (What a legacy, eh?)
As far as the bunker not being very good protection against a nuke, we school kiddies of the time were being taught to duck under our desks and cover our necks when we saw the flash of a nuclear explosion. If THAT was good enough... just imagine how cool a concrete-covered bunker was.