If he bets on himself and wins, is that *really* a problem?! As if he'd go out and purposefully Lose otherwise?!
Golf isn't like a two team or two person game; one person doesn't control the outcome. If Tom Willis bets *against* himself in the Tour de France, would anybody care?! Heck, the only interesting thing about some nobody betting against himself in some sport like cycling or golfing would be HOW and WHO he managed to find a way to do it (not to call Mickelson a nobody).