I lack affective empathy (the ability to feel what another is feeling), but I have plenty of cognitive empathy (the ability to know what's going on in another's mind). Other people's emotions don't affect mine, but I usually am aware of how they probably feel and can talk it through with them, or listen to them if that's what they want. Frankly, though I know some people want other people to cry with them, I cannot grasp how that would help anything, and I can't do it. I like the way I am because I can advise my friends or listen to them vent, if needed, while keeping a level head myself.
I can't say I agree with the study, though. The people around my age who I associate with are very empathetic, in general.