Me too. I was with my best dog ever when she died years ago and I was a wreck. I was also with my mother when she died. Quite bizarrely, it was not nearly as bad for me.
I don't think the way one deals with death is so much about sensitivity or lack thereof, but more to do with one's understanding of death and beliefs or theories on what death really is.
To me, it is just the end, nothing left, no afterlife etc. I think this is why I can feel detached from death as far as the deceased is concerned. That only leaves what it means to me as the one left behind. In the case of my dog, she didn't know what was happening or even have a clue about death and we had no opportunity to discuss it. My mother, however, knew she was dying, what it meant, and we had the chance to say our farewells.
I don't feel bad about feeling worse for my dog than my mother because of the different situations. This might be the same as in the situation in the original post. Although person A dies, and persons B and C may have been equally connected there should be no morality contest to feel any predetermined amount of grief........Hold on, this post is taking a long time........Am I drunk?