Here's my guess on this:

Normally (ie. in PvE), if an enemy dies to DoT damage it is recorded in the chat log as "X is defeated." instead of "Rentho'ra Niet defeats X." However, with the Feast having its announced kills, this won't do. It has to assign the kill to someone. That "someone" is most easily assigned by taking whoever did the last bit of damage. But for the sake of argument let's say I kill someone using only Bio and Bio II - attacks that do no damage initially, but inflict damage over time. Going based on "who did damage last" isn't enough, because they would not have taken direct damage from anyone. So it seems that the logical criteria is "who affected the target last".

If you (or your fairy - pets are combined with owner for the Feast) healed the target but they die to DoTs anyway - something that is quite easy if only your fairy is healing - then you were the last player to interact with the target before they died. So... you technically "killed" them, because you didn't heal them enough?

I observed this behaviour myself when our Bard had DoTs on a target but missed out on the kill because the healer healed them, only for them to die to the DoTs and be marked as killed by their own healer.

Since there are no skills akin to "sacrifice an ally's HP to do XYZ", I think the easy fix would be to change the criteria to "who, out of the enemy team, affected the target last". This should prevent the "backstabbing" issue and award kills correctly.