I feel the need to pick a nit. While you're correct that the reason off-roaders let air out of their tires is so that they don't sink into the mud (as well as reducing the likelihood of a puncture while traversing sharp rocks), the contention that increasing the surface area of contact makes no appreciable difference to friction only applies to perfectly rigid surfaces. Car tires are made out of rubber which deforms around imperfections in the road surface, and increasing the size of the contact patch can make a measurable difference in the amount of traction available. This is why you see rear-drive sports cars, race cars and dragsters with stupid-wide tires on the back. Of course those same tires are more likely to aquaplane when it rains so it's a double-edged sword.