Or that, or her magic canceling is an active effect, that she uses in a manner similar to Ki, by 'projecting' it. She's been hit by unexpected magic before, as happened in the first chapter, so we know that it isn't an effect that is connected directly to her presence, like an aura. But, she can't cancel magic with her hands, so probably the anti-magic effect is based or centered on her artifact.
Still on Asuna, I'll be betting that Princess Arika, who I remind, is also missing or dead (someone correct me) is Asuna's mother. Which would explain Asuna being called an 'Exiled Princess'.
As for Setsuna, I hope she comes out of the closet in the next chapter.