This is an interesting discussion. Ultimately, a conclusion is reached that the energy stored during frame flex can make the wheels go forward. The experiment, however, is flawed.
The experiment involved holding the rear wheel with the brake, and deflecting the frame by applying weight to the pedal. When the rear brake is released, the frame is able to return to its normal position. Since the pedal is being held in place, and the wheel is released, the "spring" releases its energy by turning the wheel (a small amount).
The problem with this experiment is best understood in a real life situation that causes frame flex: climbing while standing. Since the rear wheel resists being turned (fundamentally because of the pull of gravity), the frame flexes when pressure is applied to a pedal. But unlike the experiment, the resistance against rotation (gravity) is not released, it stays the same. The frame is allowed to spring back because the rider shifts his weight to the other pedal. This is the opposite of the conditions in the experiment.
In the climbing example, the frame springing back cannot move the wheel, because the springing back is caused by release of pressure on the pedal, not release of resistance at the wheel. Therefore, and as previously stated, the stored energy is not available to move the bicycle forward, but is wasted.
All of this just shows how apparently scientific studies and data can easily be used to give misleading results. I don't think that was the author's intention. However, he designed an experiment to demonstrate a point, not test a real world phenomenon. This is a common problem with arguments made in every field.
Louis Schulman
Tampa, FL