"This happens in the fast and slow run and in moving from the starting blocks in sprinting. It's all the same. Our muscles/ tendons are loading in the faster run more, because of the quicker change in both vertical and horizontal directions. Then our muscles are responding (reacting) to these requests. The primary request is falling forward"
You have the cause and effect so backwards - you have greater acceleration (quicker change in directions) => greater loading => greater muscle activation (Then our muscles are responding).
I agree that these things occur together, but it is the muscle activation that causes the loading (and greater ground reaction force) which in turn causes the acceleration.
The Lean:
Standing still, no lean is required. Once you start to push your foot backward (giving a forward propulsive component to the GRF), you must lean forward a little to avoid creating a net moment of rotation about your COM (otherwise you would end up on your back). Same applies to the unicyclist example given previously. The lean DOES NOT drive the forward motion, it is means of preventing the forward drive from upsetting your balance / posture.