I believe I've seen something similar done in cycling races, where the fastest through a segment of a course or the first to an intermediate point on a course would win something. As I recall, the reasoning was that it would encourage people to go hard at difficult points or throughout the race, preventing a slow ride followed by a sprint finish. Interesting idea to bring to running, though I suspect I'd take a similar approach to you. I wouldn't sprint up the hill but it might be incentive to attack a little harder than I normally would.
Out of curiosity, how did they get the times? I would assume it was a chip timed race with intermediate mats at the bottom and top of the hill?