Similarly, Tesco dispensed with the services of the guy who was originally arrested for the Ipswich murders (but was subsequently shown to be innocent). They did so because his admissions of using the services of prostitutes, and his continued presence in one of their stores, was deemed to be likely to deter some customers from using that store.
Other employees have been dismissed because 'rumours' adversely affect their working relationship within the organisation, or with customers or clients. (If the rumours were totally without any foundation, the employee might be able to take action for unfair dismissal, but at the risk of those rumours being aired in public. If the rumours started because of the employee's own unwise actions, those actions might be regarded as leading to a 'loss of trust', making the dismissal lawful).
Chris