"You can avoid thinking about something, yet it still happens. That's entirely different than it not happening at all. Why am I being so persnickety about this? Because it makes a difference when you look at the physics of it, and that's where you can determine whether or not a claim is viable."
It's not that simple, only theoretically everything can be reduced to physics. As a former kyokushin fighter I can give you an example: in kyokushin karate contest ( kumite)if both fighters earn the same amount of points during the fight, the winner is declared by temeshiwari - that is, breaking technique: the one who breaks a bigger number of boards with his fist takes the win. Now - if you are a big and strong man, you can easily break one board, or two, or even three, and with the number of boards increasng the chances of you breaking your hand also increase. Meanwhile you can see a karateka who, being twice smaller than you, can break twice more boards or even bricks, and never break his hand. You could say it's training - but if we reduce everything to physics, such training would be impossible, because you could argue that certain tissues can withstand only certain mechanical impact, etc. The difference between the abilites of a karateka and an ordinary guy is their mental focus and determination -that is, we make things happen by THINKING they will happen. The same with walking on hot coals, lying on broken glass, etc. Of course, there are certain physical limits, but we can never know what they are. You know why you are not able to break a brick with your fist? Because you are afraid, when you stop being afraid, you are able to do it(if someone can break 5 bricks, by sheer physics I see no reason why you can't break one). The same with falling forward in Pose: your mind is afraid to fall, and you reflectively try to get a hold onto something (that is, you reach with your foot in front). It takes a lot work and drills to overcome this, but believe me - when you get it, then you know what's it all about. I remember when I got the feeling of the "free speed" for the first time ( gravity pulling me forward and me only picking up my feet not to interrupt the continuos forward motion), I didn't want to go home for fear that I will lose the sensation and that I won't be able to reproduce it tomorrow. And believe me, when you get that feeling, you don't give a rat's ass about all the vectors and such. I don't see why someone should not try it just because he can't justify it intellectualy (well, maybe I'm wrong - one has to believe to make it possible for him).
All the metaphysics aside - Huffman has answered it clearly: gravity pulls you forward, and stored energy of muscles and tendons helps to regain the lost height. All the vectors game is irrelevant. Just do the "Change of support" drill: stand in running pose ( on the balls of your feet, your support knee bent, head, shoulders, hip and ball aligned in one vertical line, the other foot under your hip), start leaning forward from the ankles ( don't bend at the waist), and when you lose balance and feel the urge to put the hanging foot on the ground - pull the support foot off the gound, and here you are - you are in running pose again, only a bit more in front of were you were. The question is: YOU HAVE MOVED FORWARD.WHERE IS THE PUSH-OFF?