Empathy is a bit different. Really try to analyze your feelings next time you see something you empathize with on tv.
Are you really sad that a kid just got killed? I mean, actually sad that that specific child is now dead, or are you sad because the SCENARIO (any child, doesn't matter which, dying is something terrible) is sad?
How do we know that's not what we feel when something happens to people we know, and the empathy is heightened because of proximity?
At the same time, a lack of empathy doesn't guarantee you are incapable of caring at all, just that the care might stem from a less altruistic source.
Basically, I think it's a bit of a sliding scale, on more than one axis, and I don't think it goes all the way to 0, whatever the circumstances.