Unless your life is in imminent danger, never, ever, run on a scene.
Running back to your truck because you need some equipment? You look unprepared, and should have either brought the equipment with you, or take the patient to the ambulance.
Running with the stretcher towards the ambulance? You look like you don’t have the situation under control.
Basically, you look silly.
Sixteen years, and I have never been faced with a situation that made me want to run while on a scene.