If you still think they were cheating but they insist that it was a misunderstanding, let them have their public fiction - as long as they stop. There's no need to drive the point home unless they continue to cheat. Giving a warning before punishing is a good idea anyway - it helps to prevent bad feelings. Players who cheat can often be stopped - by telling them privately that you've noticed and explaining that if they do it again, you'll punish them in some way, such as by docking experience points. If you decide to punish a player for cheating, you must explain why you're punishing them, preferably when you punish them.
Many GMs just dock experience points or screw over the character, and they never explain why.
If you make the connection clear, the punishment may actually convince them to alter their behavior. If you don't, they have no reason to alter their behavior. They'll just think that you're being capricious, and then they'll get even more antagonistic. If there's a problem, get your players to help you fix it. For example, let's say that you discover after the game starts that some of the characters just don't work well together.