This is quite a good split between the rather ambitious concepts of empathy, but I rather feel that "real" empathy is more than just cognitive empathy. If the other person's hurt does not hurt you then it is being faked.

One thing that can always make me feel real empathy with a complete stranger is sunburn. I am not sure why this is (I don't feel the same way about broken bones for example despite having had them myself), but everytime I see someone badly sunburnt I really feel it as though it was me that was burnt.