When you shift-drag on another person's object, taking a copy away, the object you are dragging is really the original owner's object, while yours is left behind. This is counter-intuitive.
I noticed this first in the town... I shift-dragged on Mera's sidewalk to get a copy to drag in front of my store.... The end result was me owning the sidewalk in front of Mera's store, and Mera owning the one in front of my store.