I think (not sure though) that even someone that is not the owner can trade it to you (a tribe mate maybe), and you will be the new owner.
I will try some testing and come back with confirmation or not depending on the results.
In order for the container to be considered "yours" it has to be manually traded to you via the trade window. Even if the basket belonged to a third party, as long as it is traded to you the owner flag will get reset to you.
Easiest way to accomplish this is just trade with someone, pass the containers over, and have them trade them back to you.
Be sure to reset permissions on the containers, as they will most likely be Public (the previous permissions stick).