I remember a study conducted by the military to determine what characteristics predicted leadership. Ultimately it concluded that the ability to tell a believable lie had the best correlation. Extrapolate that fun fact as you wish.
The cheats just figure this out and supply an item which is already in tremendous demand - absolution of responsibility.
Of course, over time the cheats will think they can get away with anything and go on to use this skill in all aspects of their life. And some get caught, but not enough for the cycle to stop repeating. :-)
Some people are much better at lying than others. I know because I am absolutely terrible at lying and anybody who knows me reasonably well can tell when I'm lying. And I've come across plenty of people who are great at it.
War is the art of deception and the first casualty of war is the truth.