(My other address was registered in JG I have to re-send this post.
I know since there were many new posts, perhaps still relevant. It addressed to the starter of this line.)
(1) in the case of Geni public surface there exist 'my family' but not exist 'my tree'
(2) it is a positive act to add joining family details to the tree. If you find a mistake in the added information, you can correct it, or negotiate it with the partner.
(3) to delete family branches from other people's family just because you don't like to see it is explicitly a brutal intervention against another partner's activity -- a much more severe error in the collaboration, than your supposed harm you complain about.