You are fighting my battle for me ;)
Firstly by definition: Empathy is the ability to understand and share the feelings of another. This means it doesn't require understanding of their actual issue. This is not how most people use the term empathy though is it? It is a conflation of terms perhaps.
Secondly, compassion may not be well received by those in pain. This is correct and it is becoming increasingly so that unless one is identical, they will refuse aid. This is the problem with the reliance on similarity of people (empathy) rather than understanding of the issues.
See my dog argument below.