What is meant by lightning dissipates through a vehicle's body?
The car's metallic frame stays charged and the insides stay safe via the Faraday cage until it can leak away through the tires into the ground.
If you charge both terminals of the 12V battery go up the same amount when measured relative to some third, external reference potential so they both follow each other (say rise by 1000V so there is 1000V on the negative terminal and 1012V on the positive terminal) nothing big happens. That's different than charge flowing through the battery to give you 0V on one terminal and 1012V on the other.
Like your legs. If I lift both your legs up 1000m you're probably okay. If I lift up only one of your legs 1000m you're probably not so okay.