roc is correct and, additionally, remember that part of the reason that you pick up more moisture per second while running is because while running you lean forward - by changing your orientation from the vertical, your cross section relative to the path of the rain increases as well.
whereas with a plane, it's exposing the same cross section to the meteor whether it's flying level at Mach 2 or sitting on a runway.
It's not the leaning forward (which reduces your forward cross-section), but your forward motion (which increases your _effective_ cross-section relative to the rain, which is the relevant factor in the running example.
In the case of an aircraft, since the frontal surface area is smaller than the topside area, the effect of velocity is to reduce the apparent interface.
whereas with a plane, it's exposing the same cross section to the meteor whether it's flying level at Mach 2 or sitting on a runway.