So here is the situation:

There is a party of 3 people, all looking for dragonballs together.
A dragonball shows up, party member 1 picks it up, but it goes to party member 2's inventory.
A short time later we find another dragonball but this time party member 3 picks it up. This also goes to party member 2's inventory.
Item sharing was not on, and we have no idea why this happened.

Can anyone shed some light?

Not sure. Item Sharing may have been off, but the zeni and item distribution options are still in effect, I don't party much, so I'm not of much help, but it can be order from highest to lowest or whatever it says. Like Item Distribution and stuff

Ive had this happen to me 3 times twice i clicked on the ball and lost it and once i was in a group didnt even know someone clicked on one and got it. From what i can figure from it the lowest lvl member in the group always gets the db so i stick to that theory. I believe its correct because i was lvl 46 when everyone else in group was 47 and on the other occasions the other person was many lvls behind me and i was just doing his quests while he was afk so i believe that the lowest lvl in group does and always will get the db.

Well that theory certainly fits, because we were all the same level, but the guy who got the balls had the least exp. Very good to know, thanks :)

Well, I think its random. Only if they changed that recently.