Hill used the swing draw a lot, of course, but it wasn't his only manner of drawing the bow. It worked well for quick shooting on running critters like rabbits, varmints and bigger game. If you're carrying the bow at your side with an arrow nocked, it's just a natural way to get the bow into shooting position.
However, If you look at some of the old video footage of Hill shooting, particularly his fast trick shooting, you'll see that he also used what might be called a push/pull draw, i.e., starting with the bow in a bent arm pretty much at waist level, not a straight arm down at his side, and pushing the bow hand out while drawing the string back. The push/pull is the way Bear did it as well, and one of the Wilhelm brothers. Well, both the Wilhelms did a push/pull, but one drew to his waist/chest rather than his cheek.