After reading all of the posts in this thread, I am going to post an opposing view. It really doesn't matter that AA got bad publicity from this. All passengers seem to care about is a low airfare anyway. People get kicked off of planes on all of the carriers.
The point I am making is that I don't think this incident will make any significant difference to AA's bottom line. While passengers around her were saying they would never fly AA again, would they really go out of their way to avoid AA if it meant taking an extra connection or paying a higher airfare? My guess is no.
In a day or two, the public will have completely forgotten about all of this. AA is probably just going to wait this out.