Depends. A burning surface in stasis is statically exposed. If you move the surface, if there are hidden areas to which were not exposed, then they would then be exposed upon movement, increasing the burn affected area due to the movement.
So, If I am crouched in a ball and covering as much as possible, I am exposing less area to the fire, but when I open up and move though it, I expose more areas which increases my burn area. This is a physics experiment. Ball a wad of paper tightly and see how fast it burns, but open it up, allowing maximum exposure to the surface, and it burns much faster.
It isn't perfect, but the idea that moving increasing your burn damage isn't unreasonable. Now why running would be more damage than walking, well... that one is debatable.
Why are we comparing a ball of wadded paper to a warrior standing on a burning surface trading blows with an opponent? I think we can safely say the Warrior is not "crouched in a ball and covering as much as possible". And yet standing on a damaging elemental surface fighting = less elemental damage than walking even one step across it.
