Reality TV?

Why does every sitcom always have a semi-serious episode in which someone falsely accuses someone else of something terrible as part of some ridiculous misunderstanding and then apologizes later? And the person accused is always someone who would totally do exactly what he is being accused of, but because this is the one time he isn't guilty, he feels justified in getting all self-righteous.

Like the episode of ALF where ALF gets accused of eating the family cat when it really just ran away, or something. ALF gets all offended (in English, of course, which is clearly the native tongue of all those who hail from Melmac) that the family doesn't believe him, even though every single day since his spaceship crashed into their work shed he's either tried to eat the cat or at least made a joke about it.

Am I missing something? Is this something that happens frequently in the real world? I'm honestly asking because I don't think I've ever falsely accused anyone of anything...ever. Nor would I put up with some asshole, who in the past has repeatedly done whatever he was accused of, incredulously pontificate about how hurt he is that his accusers would think so little of him. No way in hell. That little sermon would end real fast.