It can be done to everyone. Here's my theory:
You know how kirby moves back whenever he uthrows? Well, I suspect that he also does when he's on the edge, but crashes into an "invisible floor" directly level with the edge, which makes it look like he doesn't move back.
Now, any character can accidentally DI into the edge at this point, Ninja Spiking them, but only a few characters have some strange aspect about them that makes it so they hit the edge without DI'ing into it.
Also, the Character Stage Stage format is dead, as I don't wanna post all of these characters for lylat >.>
Edit: Meh, screw it. *keeps Character Stage Stage format*