Cognitive empathy: I can accurately predict the feelings/experiences of another person. This can't be "faked" - if your predictions are accurate, you have it.
Affective empathy: I experience similar feelings to another party (perhaps weakened) as a result of observing them experiencing it. This can be faked, and it can also cause problems for the person who has it.
Affective empathy seems like the thing which you describe as causing problems, while cognitive empathy seems like the thing which is useful for building better products.
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.