hi, %player% returns the NAME of the player, not the uuid, on death, you are adding 1 to the attackers UUID.
uuid and player names are totally different.
code
on death of player:
add 1 to {kills::%attacker's uuid%}
actually sets the value, lets say notch.
notch's uuid is "069a79f4-44e9-4726-a5be-fca90e38aaf5"
and you are adding 1 to "kills::069a79f4-44e9-4726-a5be-fca90e38aaf5"
but the /stats command returns variable "kills:Notch". (player name is Notch)
so you should be adding 1 {kills::%attacker's name%}