While I completely agree with Tim Nevins' answer, I wanted to throw some simple mathematics in here so we can see where the truth is ...
On this website they talk about the contact patch of a P225/60R16 tire. They state the total road area where the rubber meets the road is calculated to be about 147 square inches with the tire at 32psi. If we were to calculate the area of where the rubber of the bead meets the rim, I think the following could be a fair approximation (as I don't have the exact numbers in front of me).
- Rim Diameter = 16"
- Tire contact area ~1/2" around circumference of the rim
- Tire contact area ~1/2" at the side of the bead (lip of the rim)
- Two beads
- Circumference of the rim = 16 * π or 16 * 3.14159 = 50.26544
- Tire contact around rim = 50.26544 * 1/2" = 25.13272 square inches
- Tire contact around lip of rim = 50.26544 * 1/2" = 25.13272 square inches
- Square inches per bead = 25.13272 + 25.13272 = 50.26544 square inches
- Two beads per tire = 50.26544 * 2 = 100.53088 square inches
- Four tires per car = 100.53088 * 4 = 402.12352 square inches
Compare the total contact patch area of 147 square inches to the total amount of just over 400 square inches which attach the tire to the rim and I think it's obvious your original conclusion has holes in it. Please note, this doesn't take into account the friction which is produced from the weight of the car as it rests upon the contact patch, nor does it take into account the force applied by the steel band which keeps the bead seated upon the rim. Still, though, if we are looking at just contact of rubber to its mating surface, the area of tire to the rim is quite a bit more than the amount of tire which actually touches the ground.