I'm not angry, so why do I need to settle down? I just notice a trend, and therefore I ask the question.
EDIT: Consider this...you state that the officers handled it wrong, but then say you don't know how you would have handled it.
Unless things have dramatically changed in the 16 years since I was a LEO, the police officer is not bound to arrest everyone they see breaking the law. There is such a thing as "Officer's Discretion" in play every day. If there wasn't, there'd be a heck of a lot more arrests - enough to create a police state - and your judge/prosecutor wouldn't be very happy either.
If I were the LEO on that call I would have no problem at all with that woman holding a gun on a criminal. It's woman vs man after all, but even if it were a man I still wouldn't have a problem with it. I would have identified her, taken her statement, and transported the thief to jail. Simple as that.