I just looked through the Brady Games guide, and it made no mention of Kary using Firaga (though, it's not the most informative guide ever written).

FFOnline might have assumed that, because Kary is a strong Fire elemental boss, that she has Firaga in her repertoire. Or they could have mistaken Mustard Bomb for it, like I did. The walkthrough you linked to could very well have sourced the information from FFOnline - it's a popular site.

I can't tell for sure, and I don't have a save lying around that would enable me to fight Kary in a reasonable amount of time, or I'd check for you to see if it was a glitch in your game. I don't think it is, though.