All I ask is where is the anchor the rider pushes from?
Every action has an equal and opposite reaction. If the rider pushes down then his body is pushed up. The anchor is dependent on the position. If the rider is positioned to push straight down then his weight and arms are his anchor. He can easily out push his weight so his entire body is used through his hands, arms, torso, core, to anchor him to the bike. If he is positioned aft, he can use the saddle as more of an anchor, ala Greg Lemond style pushing forward then down, from his book The Complete Book of Cycling. The rider uses less energy to anchor and is able to apply more to the pedal. More thigh muscle is used making for quicker recovery from harder efforts.