This is a nice description of what it's like to take a push with a coordinated mind and body. You use of the word "intent" corresponds to how I use the word "mind". The use of intent (mind) quantitatively enhances the person's being pushed ability to effectively deal with the force of the push. To experience how this feels simply perform the test while letting the mind wander, in your parlance, direct your intent elsewhere. Your ability to manipulate the force of the push should be markedly reduced.
It actually augments the structural model described by Chris. Via the use of mind/body coordination it gives rise to a more complete model that integrates the strengths of the physical and mental to form a sort of meta-structure that is capable of more than just resisting an incoming force.
the reason why we use the word intent instead of mind is that everyone has a mind, unless you are a mime then your mind is in an invisible box. intent is an action of the mind where the mind is just a reservoir which powers the direction/vector of. the intent along with relaxation allows your body to microscopically readjust/reconfigure itself to the right structure or the meta-structure that you spoke of. of course, we are now venture into the lala land, where we will sing and dance naked around bonfire. intent is the ki (pun intended). when my youngest son was a wee babe, still in diaper. one time while driving, i saw his face, in the rear view mirror, with a such intense focus expression of highly focus intent, then he grabbed his toes with his baby hands and giggled. i immediately rolled down all the windows. my wife said "what are you doing?....arrrggghhhhh oh god! what did he eat?!!!"