As pointed out, I have no desire to derail the thread with a discussion on semantics - I think we all have our own specific definitions of sympathy and empathy - and mine remain unaltered by anything I have read on this thread.
My view is coloured by my experience with dealing with a Caller when I was a Samaritan volunteer - the lady advised me that she just miscarried, and needed to talk to someone about it. She then asked me if I was able to empathise with her feelings. My response was that honestly, know I could not empathise, I could not know how she was feeling, although I would do everything I could to understand, as far as I was able. She told me that she hoped that would be my response - and that if I had told her that indeed I did empathise, she would have put the phone down, because I was obviously not someone with whom she felt she could communicate. My sympathy was welcome and accepted, but my notion of 'empathy' would have resulted in our conversation ending there.
As I said, we all have our definitions, some, as mine, based on direct personal experience, and I think we all remain unlikely to change our positions.