Moose, I wonder if we are at cross purposes on this. The rest is held onto the bow, with a bolt that screws into the "button" hole, yes? The hole for the button is the same thread as the one for the long rod, at least is is on all the bows I have had.The hole in the body of the rest isn't threaded and is bigger than the button hole so the bolt is loose in there.
Some rests have a second hole to accept another bolt. That bolt usually has a nylon tip and is used to tighten onto the riser, without damaging the finish too much, if the riser has just one button hole. Some risers have two button holes and the rest can be fitted with two ordinary bolts so the rest doesn't turn in use.