If the pohlese were not there, they did not see her swing the bat. They go on evidence: the evidence were bruises on her, not him, from what you tell us.
Based on that and the real physiological differences between a man and woman (men are twice as strong and 10 times more prone to physical violence, studies show), police rightly make those assumptions and have to arrest someone. If only to asssure that the two are separated for at least a night to let things cool off. That is the way they operate and until someone can find a better way, ah say let them do their job as distasteful it is to us and you and we.
It is very easy to blame/question the pohlese but give them a break.
They were not there until after the so called alication.