Don't politicians know they are being recorded?

This is not aimed at any party, or any person in particular. Just an overall statement. It is soooo annoying when someone in the spotlight says something one day, then shortly after, claim they never said that, and now say something completely opposite. The Daily Show with Jon Stewart loves showing clips like that. It's so easy to find. I don't think there's a politician who *hasn't* done that...

Don't they realize that when they talk on camera, it's being recorded, and it's possible to go back and rewatch that recording at a later time?