"Maybe the same way that you can have a psychopath, you can have the opposite? Someone whose brain is hard-wired to be more empathetic than normal?"

Something like this maybe:

http://en.wikipedia.org/wiki/Highly_sensitive_person

Even more interesting, is this model that describes how some of the negative stuff (shyness, nervousness) related to having high sensitivity can be overcome by the subset of that population that go on to accomplish great things:

http://en.wikipedia.org/wiki/Positive_Disintegration