to one side of the horse in order to keep from being shot is historically accurate.
As an example, during the Posey War of 1923 down in southern Utah. Chief Posey did the same thing while evading a posse. And while it typically worked, in Posey’s instance he was still shot (through the hip as he adjusted his grip/position and was temporarily exposed) and later died from the blood poisoning/infection of the wound.