I "jog" on my mini trampoline when I get too anxious or stressed. The physical activity dissipates the stress. As little as 2 minutes can help me get to sleep at night, the time when my mind can keep me awake. During the day, it clears my mind so I can make better decisions.
I don't see it as a crutch; it's more of a necessity, a tool I have in my HSP tool box that keeps me out of emotional overwhelm. Perhaps that's how running helps you.