Despite Bone-Eater's passivity and proclaimed innocence, you do need to kill the Bosmer to claim the bounty; Agronak's opinion of you will see a stronger improvement if you lie about the Bone-Eater's viciousness however.
The following Journal ID and Index codes can be used with the Journalconsole command to manually update the quest to a certain point.
Bounty: Bone-Eater (TR_m4_And_Bounty_Boneeater)
Index
Finishes Quest
Journal Entry
20
Agronak gro-Dumag, in the Andothren Imperial Commission, has told me about a bounty on something called the Bone-Eater. It lurks with its followers deep in the wilderness west of Menaan. I'll have to find them first to collect the bounty.
25
Finishes quest
I've given up on hunting the bounty for The Bone-Eater.
30
I've slain the Bone-Eater
40
Finishes quest
Agronak gro-Dumag paid out the bounty on the Bone-Eater.
50
Finishes quest
Agronak gro-Dumag is dead. I can no longer collect the bounty on the Bone-Eater.