"As the walker begins to move, she or he receives raindrops that would have fallen in front, while missing the drops that now fall behind. This creates a balance, and ultimately, the amount of rain received on horizontal surfaces remains unchanged, regardless of the walking speed."

This is wrong. The back, stationary or moving forward does not receive rain. When stationary, the top receives rain(ideal model). When moving forward, the front AND the top receive rain. I don't see the balance they are claiming.

I just remember watching a Mythbusters episode where they concluded that walking kept you more dry.

This predicament is the Richard Feynman Sprinkler of urban living. Use an umbrella.

All of this assumes the rain is falling perfectly vertically. Some trigonometry will show that in the case of a tailwind, where the rain is at your back, a scenario is possible where there is a finite speed beyond which going faster will cause you to intersect more raindrops, rather than fewer. Calculating the precise numbers is left as an exercise for the reader.