An honest read of Jim's comment can only lead one to recognize that the said lack of extra backward movement on a treadmill is in reference to the belt of the treadmill. Jim is entirely correct. The only major difference associated with running on a tread mill is the chonic, speed-matching, relative tailwind (unless you are running into a fan of course).
The arguments generally made to support the POSE method are of the same type as those made for a perpetual motion machine--resting on slippery ground.
Some Thoughts:
1) Gravity pulls only down. This seems to generally accepted so no need to argue more on that point. Some here are getting into trouble when analyzing the next part of the POSE argument, that mechanical advantage can be gained by "falling forward." This will be the next point of discussion.
2)The so-called falling forward effect is a result of 1) braking by the support leg so that the body tips forward because the top, non-braking portion of the body (ignoring wind resistance) has inertia and therefore tends to continue its forward velocity, and 2)the drop in the body's center of gravity (COG)as it tips forward. Here is the first set of mistakes the POSE advocates are making.
A) The mechanical braking with the support leg to cause/allow the tipping has an energy cost.
B) Any drop in the COG while tipping forward must be completely payed back for the next stride, otherwise the COG would continuely drop and end of on the ground. In other words the greater the drop in COG, the greater the vertical drop the greater lift and therefore energy expenditure required to reset the COG. So, any falling you do, you pay for energetically.
3) Pulling up with the hamstring up has an energy cost. The POSE advocates will argue that by pulling pull up with the hamstring ground contact time will decrease and therefore less elastic energy will be lost. This may be true, but making the hamstring work more requires more energy. So, the POSE people would be required to show that the gain in elastic energy more than off-set the energy cost associated with consciously pulling up with the hamstring.