Quite an extreme example, but as I tried to show theoretically there is actually not so much bending of the ski taking place in skiing a flat surface. Look e.g. a the front cover of ultimate sking. Extreme edge angles, but the ski is not bent more than what could be done with one hand. Most of the force is under the foot.
Edit, picture insert did not work, URL: http://www.ronlemaster.com/Ultimate_Skiing.jpg