While she didn't need defending, it was likely a politically useful thing to do. In this setting, men are treated as stronger than women, so if the duke didn't protect the duchess it would lead to possible rumors of them not being on good terms(after all, 'why else would a husband leave his wife to fend for herself' would be what they think). And since currently the duchess's power mostly comes from her marriage(for now) that sort of rumor would weaken her position.
Just want to note about "taking from top"/"getting a share" - as long as it's indeed from top it's often easier for superior to simply turn a blind eye than replace you. While majority of this guys put their hands in core funds which is never acceptable. Like IIRC duchess chose her snitch by the simple fact that he didn't done anything that would require sacking him - unlike majority of others.