I remember a BAS-mission made by Nagual where the "killed by" text was replaced with information on where the person was shot and with how many bullets. Example:
"nominesine was shot in the head by Acecool"
"nominesine was shot in the torso by Acecool"
If you can alter the text I suppose you can also remove it. The mission is named "Kimbe Assault" and it was released as a MP-mission together with the BAS_Tonal+Opfor pack. Download it, unPbo it and see how Nagual did the scripting. It's not a feature of the BAS-addons, I've never seen it in any other BAS-mission.