Public Figures and Defamatory Statements

Last class we discussed defamatory statements and how public figures have a harder time proving falsity. Now my problem or rather the thing I can't get my head around is how a public figure would potentially have a harder time proving falsity in every case. One example could be someone is accused in a tabloid news story of sexual misconduct at a club, on the same night they were taping a music video somewhere else. Well in this example falsity can be proven by time stamps on the video, dozens of witnesses, possibly even security footage, and the call logs of the cell phones. Another example deals with a private figure who publicly, meaning by name, is accused by a friend or fellow employee's wife or girlfriend of sexual misconduct in an advice column. In the latter scenario it would be easy to prove falsity so long as the accused doesn't have a common name and malice was intended by the public accusation. The problem with falsity is people can lie and lie detectors are fallible.