Sometimes you can prove an alleged event did happen, but you generally can’t prove something did not happen. For example, if police have clear video footage of a crime in progress, several direct witnesses, and DNA evidence too, you can say they proved the defendant did the crime. But if your neighbor says an angel visited him in his bedroom at night, and there were no witnesses or physical traces left behind, you can’t prove it didn’t happen. All you can say for sure is that you don’t have any evidence of it happening.
So if you want to drive a political opponent crazy, allege that he or she did something evil, provide no direct evidence, and force them to do the impossible: Prove it didn’t happen.