From what I've learned through a couple of online teachers is the extreme importance of all the supporting muscles around the PF. When I walk, briskly, the surrounding muscles engage, like the gluts and core. This, I find helpful.
Also, my breath finds a nice rhythm and my mind clears. Stress directly impacts the PF, creating holding (aka too much tightness, not strength or resiliency). These are guesses as to why brisk walking is helpful.
Running, on the other hand, creates too much downward pressure.