What makes the police so adequately qualified to sort these things out? Unless there is a real pattern and something that is actually verifiable, even if it's true, sometimes we have to let bygones be bygones. A single isolated he-said-she-said incident is a sad turn of affairs but not worth the publicity that it would bring.
You are aware that you are describing the status quo of the organization.
I'll bite. The single isolated he-said-she-said event is a sad turn of affairs that should be turned over to the police. Whatever the publicity, the intent is to prevent corruption and to explicitly put the individual ahead of the organization. At the very least, advise the accuser of the option to do so.
The status quo abhors bad publicity and explicitly puts the organization ahead of the individual.
I don't actually have a great answer to the objection that the accused person can have his or her reputation jeopardized. On a personal basis then, you have to protect yourself and be cognizant of any appearance of impropriety that could be used in an accusation, just like anyone else regardless of position.
I certainly don't want the legitimacy of an accusation to be investigated by representatives of an organization that is against the higher education that would qualify them to do so.