When Bud Searcy makes his miraculous shot, it is the character on the right that falls to the ground. The previous shot showing Lizbeth and her Indian captor clearly show the Indian on the left from the perspective of Bud Searcy.
Towards the end when Bud Searcy makes his miracle shot at great distance, the Indian falls off his horse the instant the trigger is pulled. At that distance there should have been a slight delay.