The pet being "dead" wouldn't fool me anyways. Actually sure let the pet FD as well as the hunter, would actually mae most non hunters life easier. And the pet still hitting me is not what gives it away when a hunter FD's, it's the fact there is no "KILLING BLOW <insert random hunter name>" popping up in the middle of my screen.
Basically this change would probably only be a setback to hunters rather then any help.