No, its not insensitive. It sounds like you have a lot of those birds anyway, sometime having one less helps. Lot of work even though you still try to save every last one. :) It is all part of natures cycle.
The only thing that I can come up with is the duck died of a heart attack. I had a silky die that way, she was having a dust bath in her favorite hole, she was 9 or 10 yrs old.
Edited:
Maybe a stroke, don't know how you could check that.
Just went through the whole thread and was wondering if your chicken is still in the fridge....... This was very interesting and educational, :) thank you!!