That is ridiculous, especially in archery season. Not to many shots with a bow will drop them in their tracks. Generally you have to spend some time waiting for them to die before you go after them so they don't run farther. Better to make a good track with two sets of eyes, than to run right were you think the elk is only to find you were mistaken and have to start tracking again. My buddy did that last year and almost lost his bull, he was in the wrong area looking for an elk for hours because he rushed in where he thought it was.
If you made a good shot that was fatal, that elk is yours period.