Did AA match that fare on any dates that are acceptable to her? If so, you should be able to at least change the AA ticket and get something back, less the change fee. But you wouldn't have to buy another ticket and be out of pocket.

Failing that, I would chalk this up as a lesson about nonrefundable vs. refundable fares. you might introduce her to farecast.com (now Bing Travel) to help plan better in the future, although I don't think that FAI is included in their predictions.