I added the death counts in that trigger's conditions. If your teammate is dead, enemies aren't and you got kill score, you backstapped him.
I tested it in your map and it works now.
If both teams teamkill at the same time, nothing happens... (to make it totally equal you should add a negative points counter.)
I send u the map per PM.

Confused why my map isn't working, I thought I had this right but I don't. The triggers are commented "Red kills Orange" "Orange kills Red" and etc.

P1/P5 (Red/Orange) are on one team, P2/P4 (Blue/Teal) are on the other. Any help would be appreciated, thanks.

http://www.mediafire.com/?et0fdozjedn

Fixed it. Strange bug though, even though I had the backstab triggers first, the "player kills enemy" trigger fired first. I guess the "deaths" isn't recorded as fast as the "kills" score. Whatever, it works by adding additional conditions to the "player kills enemy" trigger.

Exactly.
Dying units can still be detected for a half trigger loop or so.

Yeah, by the Bring/Command conditions, however, as soon as they die the Death is added. Hence being able to detect where a unit died. Something else must have done it, but it works anyway, so