I agree with you Liadan.
As for the 'extreme act of spontaneous anger' and the comment "if he had stopped to think of his children' I would say that is exactly the point. A person who loves their children and who has a conscience does stop to think about them, or more likely doesn't even get to the point of such extreme anger that they would be on the verge of actually killing someone and need to 'stop themselves'.
Someone who is a narcissist is incapable of really loving anyone, and this includes their children. Some people are incapable of real love. Just remember, love is not a feeling, it is to do with actions. If you can't demonstrate your love in the most unselfish of ways, then you can't love properly, and you are no good to those you 'feel' love for, in fact there are many ways you could harm them.
Just because we see someone crying at a funeral, looking genuinely distressed, and clinging on to their children, does not mean they can love these children in a way that is ultimately beneficial for them, and does not necessarily mean that they feel sad for the person who died. It could mean something totally different, such as an immature, narcissistic man, who is feeling dreadfully sorry for himself, who is clinging onto his children as a shield, and appreciating them in a different way, as the only ones left who, in their purity and trustingness, treat him as innocent. IMO