That's the only explanation I can think of. She just doesn't believe that anything could possibly belong to anyone to such an extent that on her whim, she shouldn't have the right to take it, play with it, or destroy it.
The funny thing is, she seems to have a pretty good grasp on certain things belonging to only her ... it's simply the idea that someone else might have that same sense of ownership that she finds baffling.
"What's mine is mine," seems to be her motto, "and what's yours is mine, too."
Perhaps she's not a communist after all, but a tiny little authoritarian dictator-in-training.
Clearly we're on the wrong train.