More than allowing self-defense of the saving of another's life, the Bible (Hebrew anyway, I'm no expert in the New Testament) and associated writings (the Talmud, which interprets the Hebrew Bible) indicate that it is required. Failure to save your own life when you can is stealing from G-d. He gave you a life for a reason, so that you could develop your soul and make the world a better place. To so carelessly throw it away is to throw away a priceless gift.
Another way of looking at this is how Jews look at the subject of death as related to the soul: basically, physical death ends the ability of the soul to do good deeds, to learn from moral errors and to teach others how to do good instead of evil.
Yet another way of looking at this is the following: The Talmud indicates that each life should be looked at as if it were the whole world. Why? Because the world would be different if that life didn't exist, thereby "destroying" the world in which the life did exist. Hence the saying that "he who destroys one life destroys the world, but he who says one life saves the world." In the case of this idiotic and amoral/immoral woman, had she and her son been murdered due to her failure to defend herself, she'd have been guilty of destroying the world twice. OK, I'll give her a break - maybe she was so naive before the incident in question that she had no gun. But after this, to refuse to defend yourself and your family? And to publish this BS story, obviously intending to influence others to do the same - how many others will fail to defend themselves because of her story? How many others will not be as lucky as she and her son? How many worlds will she destroy?