Nothing to do with physics, the runner themself exerts more force.

Yes he exerts more force (well more energy anyway) to compress the shoe which happens more slowly than it would barefoot so the force exerted onto the body will be less than it would if the same energy were applied over a shorter distance/time with either a thinner sole or no sole at all. The problem with cushioning is that it may alter your running style so that you run with a gait which is not natural for you and so leads to "unnatural" stresses and strains in the legs and so leads to injury.