I checked, and it doesn't leave it as a failed quest in the filtered Journal. Unfortunately, I did not check and see if it left it as failed in the unfiltered journal. But the last time I played it through and did it the way the posts say to: Fail one or the other... It did show one as failed. When I did it the way I said, "Following the Fat Lout dialogue a couple of times until Balin Attacks me" I received lots more XP, did not get a rep increase, and the quest was shown as completed...
Try it out and see what happens.
Hmm, I'm not sure, but I think I'd take the reputation increase over the experience. Although that is definitely an interesting way to complete the quest, thanks for pointing it out. If indeed both quests were shown as completed then that is interesting, since there is only one necklace...
