How should the top edge of an asphalt shed-type roof be finished?
That's at the PEAK of a shed roof, true? If that's the case, what you have amounts to a ridge cap, but nobody I know of manufactures premade ridge caps for shed roofs (too many different possibilities, not enough market), so the builder used "drip edge" or flat flashing (bent around the peak) to function as a ridge cap.

There really aren't very many good alternatives to that situation, so what they did is actually pretty common on the peaks of shed roofs. They really SHOULD have tarred over the nail heads, though.