Caveat: run flat tires do have stiffer sidewalls that become compressive load bearing when the tire loses air pressure, in that case, the loading is compressive and pushes upward on the rim. But even those are highly limited in loading--further evidence that in tires, the tensile stress is the dominant load path. Also, when inflated, the hoop stress on the tire is greater than any residual compressive stresses applied by the sidewall between the rim and ground, so under inflated conditions, the carcass is under purely tensile loading.
Other run-flat (foam filled or inner ring) tires also operate in a compression loading mode when not inflated.
