It's an interesting study. One thing I'm not sure about is: were the participants in (any kind of) pain originally? Was it chronic, or acute?
Intuitively, and from my experience of 15 years of fighting with chronic pain, it's incredibly hard to emphasize with anything at all when you're in serious pain. It's hard to even think about anything other than pain. I'd say - again, from the perspective of a chronic pain patient - that reducing the pain with medication makes it possible to have empathy towards others. Obviously, I have no neurochemical data to back this up, I'm just saying how it looks like to me, psychologically.
If I had to guess, I'd say that being in pain does little good for empathy and it's a memory of being in pain that counts. When I'm in pain I'm not going to care too much about yours, but when I was in pain, and I remember it clearly, I'm going to care a lot.