Earlier quoted context omitted.
In other words, running in the rain gets you more wet, given that all running is doing is reducing your exposure time. (Yes, sometimes that exposure time can result in you coming out ahead, but it's not really answering the question) EDIT: What the hell's with the downmods? What is this, reddit?
If I've parsed that correctly, you're wrong. The following are true: For a given amount of time, running in the rain makes you more wet. For a given distance, running in the rain makes you less wet. Running reduces your exposure time by more than the increase in rain_per_time. Perhaps I've simply mis-understood you.
My point is that reducing your exposure time is basically altering a different variable in the equation.
If you control that variable by not running to a place where the exposure to rain stops, it becomes clear that by running you will get more wet than if you were simply walking.
And yes I understand that practically, running to a dry spot is the whole point.