There are several assumptions made there, that I believe you are wrong in, Andy.
First of, an insult does not warrant a challenge at all. If that was the way, noone would dare say anything, because people could choose to take insult at even a mispercieved slight and then suddenly you'd have a duel on your hand with the insulted part choosing time and weapons.
Imagine the Green Knight turning to you, after you just congratulated him on a victory and state "You said what about my mother? Insult! Duel on swords tomorrow at noon!" It might be exaggerating, but it might also not. If you consider an insult a challenge, I have the first 4-5 duels I need to deal with. Take it to the realm-levels: Would you consider going to war, if the OIT called the Haelyn's Aegis "stuffed up pretenders"? It's an insult...
As it it, you can use insults as the baron did here, to pick a fight. The Swordmage could have shrugged and left. Had she done so, the Baron would just have come of as a hotheaded man and most would have scoffed at his bad manners... as it is, the Swordmage challenged him, assuming that he would back down, or that she could easily beat the elderly man. She issued the actual challenge, and by doing so became the aggressor and fell in the barons trap with both legs and eyes wide shut (as Alex put it). It was a brilliant move... and though Kaven does NOT appreciate the way things happened, it did happen by the book.
Secondly, the only group who have recognized her as a duchess (to my knowledge), is the temples... but since they aren't a secular power, they might have influence in the matter, but no final say. If you held a council between the gathered nobility at the moment, my guess is, that the Swordmage would be officially stripped of her "title" (though it'd probably be a challenge to actual sieze anything from her.)
Thirdly, she's a reputed sorceress and warrior (heck it's pretty recent that people discovered she was a female, right? Or is that just RoE II canon?). When she challenges someone, they usually have something to fear.