When someone tells you a lie that you can clearly see is not true.
When someone says, We aren't interested in reading your emails or listening to your phone calls. We're just curious about your calling patterns. That is a governmenttruth. OR A guy's wife comes home to find her husband having sex with another woman and he tells her that it is not what it looks like.
Saying something even worse then what actually happened (still usually bad but not necessarily) to subvert expectations and make someone less upset about the second thing.