So I presume HR had a chat and offered them a pile of money to resign - or if they didn't accept, indicated there would be an investigation into their behaviour.
Presuming they didn't choose option 2 and lose - when asked, nobody's going to say they left for sexual misconduct.
It saves the company some paperwork, and weakens the employee's case for taking them to court for wrongful firing. In exchange, the employee can truthfully tell future employees they weren't fired.
I think so; since they weren't charged with a crime, I guess privacy comes into play.
That said, if someone was sacked for sexual misconduct, nobody would hire them if they end up working with women. (I'm aware I'm gender-stereotyping here, but unless I missed it, all allegations were from women aimed at men. As is often the case.)
Would it be illegal to ask if they were fired in connection with this push? If the candidate answers no, they’re clean or a liar. If they demur or confirm, you have your answer.