I used be able to watch videos/view images of the goriest and most explicit nature: brain avulsions, total dismemberment, horrific murders. In fact, I craved viewing them. There was something in there that was fascinating to me. This was when I was much younger. As I got older, these pictures began to bother me. Not because I felt guilt or empathy, but because I had suffered accidents/injuries of my own, and they served to remind me of them. Now I avoid them, for the most part, because in each body I see the inevitability of my own mortality, and I always end up relating them to my own situation.
The same holds true for emotional pain: just yesterday a girl related a story about a woman who's mother was killed by a distracted drive. I laughed when I heard the specifics; it sounded like such a glorious explosion of metal. Everyone else was horrified, and some were holding back tears, but I couldn't stop grinning--I had such fun recreating the scene in my mind. I couldn't empathize. But if another person's emotional pain reminds me of the few, and I mean 2-3, things left from childhood that are still painful to me, I am distracted and lost in my own pain. This gives the appearance of empathizing; it's not. I don't cry for the other person; I cry for myself.
That erroneous conclusion ("They're crying while I'm crying; they must understand me!") is what, I think, leads empaths, especially those with emotional ties to the sociopath, to insist that they're "not that bad" or that "there's really deep feelings in there." Perhaps. But those deep feelings will always be self-centered. If a sociopath cries because you're breaking up with them, it's not because they've suddenly grown a heart to pine after you with. It's because they've lost control, because their plans have been ruined, and they're thinking about how the break-up will fuck things over.
I realize they are interesting, and perhaps very fine distinctions to make, but I think that they are actually legitimate distinctions to make between a sensitivity (or lack of sensitivity to things) and the general skill of empathy. A good example, perhaps, is the one of the typical empath who becomes desensitized to things like violence in times of war. According to wikipedia, horses, who have a natural fear of unpredictable movement, become desensitized to accept the fluttering skirt of a lady's riding habit. We sensitize guide dogs to certain human concerns like automobile traffic.
Everyone can learn to care more or less about a particular thing. It's not that sociopaths are just constantly choosing not to care. I believe that they are partly incapable of caring, and even more simply unaware of what and when they should be caring. Once you direct their attention to it or something else happens to make them aware of the seriousness of something (e.g. growing older and having more a sense of one's own mortality), it gets easier to understand why everyone else is upset. But this does not mean that the sociopath will ever vicariously feel what the other person is feeling.