Historically, this is exceedingly rare. Nobody wants the negative attention that comes from exposure of a false allegation.
In EVERY instance, I was treated like a piece of garbage until I managed to produce my recordings from storage. I have become increasingly paranoid about being around people because of this.
This part is not the problem. The problem is that if you're falsely accused, it's on you to prove that you're not a horse, which will require enormous effort or an unusual foresight.
A similar thing to the problem in US of stealing identity. If somebody impersonates you and takes a credit in your name (and you have no control over that, because your personal data could have been lost by some Equifax), suddenly it's your problem to fend off debt collectors.
Yet if you're a male, you can still end up falsely accused of sexual harassment, because she didn't like you, she wants your position, she misunderstood you, or she was just a bitch who likes undeserved attention, ruining somebody's life in the process. There were examples of that, and while I don't claim they were numerous, they are the source of the chilling effect.