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You're right about the case head being against the ground which would act like a breech face/bolt and prevent it from backing out of the tire tread, which would also give it some measure of support. However the tread thickness is probably about as thick as the height of the case web at the head. That portion of the case is actually strong enough by itself to contain the pressures of firing which would be between 55-65,000 PSI. The front part of the cartridge case however is much too thin to contain the pressures and would simply explode which wouldn't produce much energy/velocity.
It would be a lot like ammunition going of in a fire. People think it's like Hollywood and bullets go ricocheting everywhere. As usually is the case in movies and TV they are totally wrong. The ammunition just pops open because the case can't contain the pressures without the support of the chamber. The resuting bullet/case fragments won't even penetrate drywall/sheetrock most of the time. Of course a loaded gun in a fire is a whole different ball game!
Regardless I hope I'm never driving around with a loaded shell in my tire!