To test this for yourself, go out and run in place, not pushing, only lifting. Now, Lean backwards. Then, lean forward. Remain only lifting. Did you move? Why?
The concept is similiar to balancing a pen on the palm of your hand. let the pen start falling in one direction. If you move your hand in that same direction, the pen maintains its fall. In running, you maintain a sustained falling and changing support with your feet landing directly under your hips is equivalent to the hand remaining directly under the center of mass of the falling pen. People with poor running form often fall at a great degree, but stop themselves as well with heel striking and overstriding.
You can also go aqua jogging. Only lift. The extra resistance from the water will not allow your support leg to fall completely. The faster your turn-over, the less your support leg will fall. You will be able to feel if you are actively pushing. Only focus on resistance of water on the heel of your lifting leg. Lean forward and you will go forward. Stop moving your legs, and your face will fall into the water. Lean back and you will go back. Stay straight up and down and lift your legs and you will stay still (note, a aqua jogging belt will cause you to go forward still, so you have to lean back some). You may argue that even when 'only lifting' you are still pushing some, just not as much, just as people argue with Romanov running on ice. Video tape yourself with just a 'slight' push, and your leg will not be lifting under your hips fast enough, the equivalent of the hand not moving under the falling pen fast enough. But, unlike the pen, you don't fall on your face, you overstride to compensate and stop your falling = injury. When in the water, you will see that you can control speed with your leaning, without pushing.
You can argue the theory of it until you are blue in the face, but I have a large group of people I train with who look great, are injury free and practice every day to get closer to perfection. They had trouble understanding at first, but now that they are running with this method everyday, they know it is the truth behind running with proper biomechanics. Only lift, how much simpler can it be? All running induced injuries, overstriding, heel striking, poor posture, arm cross over, slow turn over... is due to not pulling your leg up fast enough under your hips. Perpetual pulling.