There's plenty of evidence in this case, just possibly not enough to pass the threshold for a successful criminal prosecution. People get fired all the time for doing things that aren't illegal, and where there is strong but non-conclusive evidence of wrongdoing. For example, if I consistently take time off for being "sick", I'll eventually be fired, even though the company obviously won't be able to prove beyond a reasonable doubt that I wasn't sick on the relevant days.
No. The legal system codifies societal values we have. One of those values is that accusations without evidence, like rumors and gossip, are poor reflections of reality, and should never be used to judge someone's character.
Witch hunts were real, remember?