http://rationalwiki.org/wiki/Backfire_effect
I've been spending a lot of time focusing on this with customer support. When a customer is hot about a problem it doesn't help at all to show facts about anything. It really helps though to begin with a place of empathy of how you understand how they feel if you were in a similar situation. For example, had a great experience with Indinero recently when I was hot about a problem. Their customer service rep though approached it exactly from how he would feel the same way as me in such a place and here's how they'll fix it. If he just started with the "here's how we'll do better" I don't think he have gotten through to me in the situation. I've been using this a ton with problems ranging from dealing with my 2 year old to hot topics for customer support, and it's really impressive how well it works.
Yes, in many ways it's simply practicing empathy. But for some reason without thinking about the tactic folks who want to be practicing empathy don't seem to get to that point.
FWIW: I talk about this topic more in depth in video: https://www.youtube.com/watch?v=tzGOdE92z9I