And no, my position does not make any of those assumptions. My position takes into account that the person might be armed and might react negatively to someone yelling for the police. My position is based on knowledge, not assumptions. You are in your house, the potential threat is outside of your house in the back and the police are outside of your house in the front. Those three circumstances show that you are not in immediate danger and that you have access to people trained to handle potential threats. If you shoot the person, your actions are question and perhaps irresponsible.
If I were in that situation as has been described by the article, I would have either opened a front window/door and shouted to the police or I would have called 911 again and told them to tell the police outside of my house the situation. I would have my gun and watch the person from a place where I know they can't see me and if they tried to come into my house or if they pointed a weapon, I would shoot them. That would be the responsible thing to do and you shouldn't have a gun unless you know you can think that way in these situations.