How accountable should you be held for your subordinates' actions? (Urban Meyer)

Urban Meyer is on paid leave while an investigation is being conducted to see how much he knew about a former assistant coach (assistant coach was recently fired after being charged with a misdemeanor charge of criminal trespassing) who allegedly beat his wife. I don't think this assistant was ever charged for domestic abuse, but it seems likely that Meyer knew about the alleged abuse.

A lot of people are saying something like "So a guy beats his wife and his boss may get fired?". Others are disappointed and think Meyer should be fired.

I don't want this to be a discussion of the Urban Meyer situation. But in a more general sense, how responsible should a boss be for one of his/her employee's actions outside of work?