There's a reason they arent admissible in court. And by your logic as long as 3 people come up with BS accusations against someone they should not be put in office regardless of whether they're true or not. Someone on 4chan could organize 3 people to come forward and accuse a random politician, and because of your 3 accuser rule they'd have to be automatically dismissed from office.
Why does it matter that they are unproven? Is that a serious question? That's ALL that matters. Either you prove it or he's innocent - but when you go public like this, regardless of whether you have proof or not you already ruined the name of the accused. That is wrong. And I dont see an issue with the audience behavior here. I mean, what's worse; Making baseless sexual assault allegations that you can't definitively prove and which will ruin a mans life, or pointing out and laughing at the inconsistencies of the accuser who's doing her best to ruin that mans life?
But you can't prove it without going public. Almost every case in court in the history of court cases is based on an accusation that needs to be proven in court. The same goes for this case, which is why a proper FBI should have been done before any questioning.