I wish people would stop saying you can't prove a negative. You can prove that you didn't do something by proving something else that logically excludes you doing it--such as being somewhere else at the time.
In this fuzzy form of what "positive" and "negative" are, there is a symmetry that allows all arguments you have for one "side" to be easily flipped. Each positive is somebody elses negative. Not guilty? Not innocent? With that line of reasong you could not ever prove anything since it's "the negative" of something else.
Mathematical logic has a solution to this though. You may want to check out constructive logic. That's where the statement "you can't prove a negative" is reasonable but has very specific meaning.
You could have programmed a script to make this comment. The elephant might be invisible. That might be your wife's identical twin sister. You can always come up with a more elaborate explanation. You haven't proved your negatives, you've just made it harder to prove the inverse. And while specific examples might be easy, in general this is hard if not impossible to do.
It would be absurd to assume your wife is cheating at every moment where you can't see with your own eyes that she isn't - no the default assumption must be that the claim is false and evidence must be presented to the contrary.
In terms of epistemology, "proof" means reaching sufficient justification for considering a belief to be true, not validity according to an axiomatic system.
(I'm not claiming that I have a solution for the problem, besides people individually waking up and realizing that it's a bad idea to rush to judgement. No amount of censorship or similar tactics could possibly solve this problem even if our benevolent tech overlords wanted to)
I believe you about it having such a standard (we can call it presence of evidence or presence of suspicion), but not on it being right.
2) Preponderance of evidence makes sense on civil suits because they are kinda inherently simmetrical. Either A loses or B loses. We would probably do better in using the standard of evidence for, say, a traffic violation, in the case of social "lets get this guy fired and try to make sure he never gets a job again" -- might not be enough of a standard, but better
Which I believe it *has*, but absolutely should not have
What do you think the highest and lowest standards of evidence should be for "social opprobium"?
And what is the maximum damage to ones life that "social opprobium" should ideally entail?