What I think American football is a good example of is a game with very well-balanced rules (though they are complex). Because of the appropriateness of the penalties, and the right of the victimized team to refuse a penalty if they would be better off with the result of the play, there is almost never a situation where it is to your advantage to get caught breaking the rules.
Compare this with basketball, where "fouling to stop the clock" is an advantageous and expected tactic. To me, any game where you would want to get caught cheating, even occasionally, needs some major rule changes! My "fix" for basketball would be that the fouled team should always keep possession of the ball, even after shooting any free throws.