Let me clarify- he IS an idiot and probably should resign. If he committed any crime (he was cleared by the student), such as improper use of a government phone/computer, he should be removed immediately.
Conduct an investigation if need be, but I am against removing public servants, because a crime might be committed against them- that opens pandora's box. Point taken, though.
Personally, I think this is a case of a guy who doesn't have both oars in the water......