Arden, the basic idea is in the whole "For every action, there is an equal and opposite reaction." A force which pulls the bar up is also pulling you down. When the lifter is connected to the ground, the "up" force is affecting the weight of the barbell and the "down" force is affecting the lifter/ground/garage/continent/etc... thus a 400# bar will move a very great distance with X force while the lifter/ground/garage/continent will move extremely little (remember that the "down" force is still only X).
At the third pull, the lifter/ground/garage/continent system is reduced to simply lifter because the connection with the floor is lost. PVC or just the bar will move quite a distance during this third pull because Y force applied to 45# also means Y force applied to a gargantuan lifter such as yourself, and that force will obviously move the smaller load a much greater distance.
Now consider what happens when the barbell is the same weight as the lifter. Z force applied during the third pull will mean the lifter moving downwards due to Z downwards force from the pull and X downwards pull from gravity. The bar will move upwards due to Z upwards force from the pull minus X downwards force from gravity. As the strength of the lifter and weight of the barbell increases, so does the force Z (and the gravitational force affecting the barbell), which will mean an ever-increasing downwards speed of the lifter and a barbell velocity which will be consistently close to zero (or whatever is required for a successful catch - perhaps the velocity could become lower and negative when the speed of the lifter increases sufficiently?).
So pulling under with the arms is a phenomenon which will become more pronounced the greater the weight of the barbell. As long as you are pulling/pressing during the third pull, it will happen automatically.
Sorry for the late answer.