Given my own experience with depression, it makes some amount of intuitive sense. For me at least, "sadness" is not wrong, but other than that it doesn't describe the experience very well at all.
When I'm really down, I can't bring myself to care about "aversive events". I might even welcome them a little bit, both because they fit my understanding better (everything is proceeding as it should be, this ant eating my flesh makes sense) and because it's an opportunity to feel something at least. For me anyway, depression is more about absence of affect than feeling "sad", and ironically it is maddening (and yet, in a sense I can't bring myself to care.)
Then again, my explanation suggests that depressed people ought to be better at avoiding harm through inaction, and I didn't see that in the abstract?
Another hypothesis is that you could stop at "Depression Reduces Capacity to Learn". It feels like all mental processing is muted, and especially any forms of change. I guess you could do a study where you have to learn to actively prevent an aversive event for someone else. But the 1st hypothesis may still apply: depressed people may still care less about harm to someone else (than if they were not depressed). But at least you could separate out whether it's only because depressed people don't care what happens to themselves.