From my experience with these things. it really sucks to be kicked out permanently for an accident. While I was not there and cannot vouch for, or against, Lavergne. it still seems more reasonable to have a week long ban for auto banning, if it is malicious TKing it will keep them out of your hair for a good while.
And if it really was an accident albeit several,
(I've had my fare share of shameful misses with an ranged weapon, and couched lances among other things, all on native servers.)
They will be able to play again after a reasonable time away, and hopeful the time will make them more cautious with their swings and shots.