So restarting the game does fix the issue with the oil barrel becoming someone else's property. I should also mention the equipment menu for the companions was buggy at the same time.
But now I came across possibly another issue. Didn't the latest PS4 patch add the feature where you can equip any armor/item no matter who is currently carrying the equipment? That was working okay a couple days ago. But not during the last time I played the game. Haven't confirmed if restarting fixes it yet.