Some would call it cheating. The perpetrators sometimes call it creative play. These players are the kind of people who think it is ok to peek at the bottom card while shuffling a poker deck to give themselves an edge, or glance at the cards in player's hands seated next to them when that player is casually holding their cards and not secreting them close to their face. They forget they have evidence that Col. Mustard isn't the killer and claim that they, "cannot disprove you," leading to your unfortunate accusation. They tell you go fish, even when they are holding the card you are looking for. They rearrange ship parts on their spaceship boards after grabbing a new part, or put parts back into the supply from their save space after finding out that they don't fit. Many of the people who engage in this sort of behavior don't believe it is wrong, they sort of see it as a game within the game, to see how much of an edge they can acquire without getting caught.
In the old west, these players could be shot. Unfortunately, we live in a more civilized time, where that sort of thing is frowned upon, no matter how much better it would make the world.
I got to thinking about this question after asking this one regarding Treasure Map. At first, I thought that the card was badly designed. Since the game's golden rule for following card rules is, "Do everything that you can," this card would require a 3rd party to verify that you don't have a Treasure Map in hand. My reasoning was flawed, because I was thinking about the card in terms of a tournament setting where monetary gain might influence players to cheat. Then it got me thinking about the large set of games with closed information. In most of those games, the designers don't expect players to have a third party verify that players aren't "playing creatively," and designers don't expect players to do so.
In an open information game, it is much more difficult to cheat. There is no information that needs to remain hidden, so cheaters can't just look at your facedown hand. Rearranging pieces that are open information is fraught with much more peril, because the cheater might be playing against someone with a good memory, "Wait, my King wasn't in check?"
What are some good ways to influence a cheater to not "play creatively" in your group? Please understand, I don't want answers like, "Talk to them, and tell them that you think cheating is wrong." Creative players don't see it the way you do, and no amount of reasoning will change their mind.
Bonus points for suggestions that do this subtlety. (i.e. "Oh, the video camera? We always record all our games. It makes it much easier to post session reports on the Geek that way.")
Edit: It might be time for some clarification. The comments, and the only answer so far seem to indicate that the only answer is to just not play with cheaters. I am uncertain how one could provide a good answer for, "how do I play with cheaters?" when one has no experience in playing with them, or has made no attempt to play with them. As an example for how it is possible to play with cheaters, I will give an example from my own past. My family is very good at Clue, and we take extensive notes. everyone records not only the cards that they have received from other players, they also indicate what player makes a supposition, which players cannot disprove a supposition, and which player did. After a couple of games were declared invalid because a player with a disproportionate amount of "mistakes" said that they couldn't disprove a supposition, and multiple players notes showed that they clearly could have, we instituted the following rule. Before saying, "I can/cannot disprove you," a player was required to pick up their cards (previously, people just used their notes marked with the cards they owned) and repeat, "MURDERER, with the WEAPON, in the ROOM," followed by their answer. Galaxy Trucker has players play with one hand behind their back, and although it doesn't prevent cheating, it makes it harder to cheat. Poker has you burn cards.
What I am looking for is people who have experience playing with cheaters, and what steps they took to help reduce the cheating. It can be general advice, or specific to a game. My hope is that someone has had some experience in this matter.