This new illusion, much more than the rubber hand one ever did, tells us about the conditions you need to feel that you own a “limb”. These include, at a bare minimum, synchronous information from sight and touch.* Surprisingly, they do not include the presence of an actual hand. Even though the brain can patently see that there is nothing there, the visual and tactile signals that it gets are so aligned that it conjures up the sensation of a hand anyway.
Our sense of "self" is more tenuous than I'd like to think.