This phrase is typically said by those trying to act smarter than they actually are. They believe that the rest of the world says the phrase "between you and me" incorrectly and are trying to show off their smart ass. However, they are just idiots.
Guy 1: (To Guy 2, in a whisper) Between you and I, this guy is boring.
Guy 2: And you are trying to be a smartass, but failing. That makes it worse.