And while I'm annoying people...
P/S/A: If you're male, you have few legal protections against women. Do not behave assuming that police or courts will treat you equally. If a woman hits you, you should consider self-defense as a last resort, and calling the police a second-to-last resort, because in either case you're likely to be arrested, and in the former you're likely to be convicted.
I would agree that in a domestic violence situation in the US, the police are more likely to believe the woman than the man. That said, the second sentence of your PSA is just a specification of the general rule that criminal courts tend to defer to police judgment in practice. Your last sentence is useful practical advise, at least right now (unfortunately).
In short, the second sentence is a specific application of a separate, gender-neutral problem with the way US society (particularly the criminal justice system) is organized. And the first sentence (...
P/S/A: There are single sentences which can create life-changing amounts of difference.