Some of you liberal politically-correct types are forgetting something here: she didn't just walk off the plane because they were Arab, she walked off the plane because they were Arab and acting in a suspicious manner. If she had walked on the plane, saw an Arab guy sitting there, and immediately caused a scene and demanded to be let off the plane, then you might have a valid argument. But that's not the case. She waited until she saw suspicious behavior. This is exactly what all of us should be looking for.
About a year ago, when I was still in the left seat at Pinnacle, I had a similar situation. About 5 Arab males in their 20s-30s were acting somewhat suspiciously. The gate agent let me know that she had noticed them behaving strangely during check in and sitting at the gate. I thanked her for the heads up and told her that we'd keep an eye on them. During boarding, the stew noticed that the men were scattered throughout the plane and were all keeping a very close eye on the flight deck door. After the stew told me that, I decided that maybe the gate agent wasn't imagining things and it was time to look into it further. I had the agent check to see where they were going, and it turned out that all of them were Pakistani citizens, but all of them had tickets to different final destinations. It all seemed just a little off to me: a bunch of Pakistani men who were talking in Arabic to each other as if they were good friends during check in, who then act as if they don't know each other and scatter throughout the plane during boarding while watching the flight deck, and all of them are going different places? Nope, too many red flags for me. I called the VP Security and he called up DHS. They pulled the guys off the plane and took them for questioning. I called the VP a week later to see what had come of it, figuring that I had probably just overreacted. This is all that the VP could tell me: "The men are still in custody due to an ongoing investigation. DHS won't say anything further, because they say the case is security-sensitive information." Moral of the story? Don't be afraid to say something if you notice suspicious behavior from Arabic men. It might be nothing, or it might be the next dry-run from a group of would-be hijackers. Keep an eye out.
This woman did nothing wrong, and she doesn't need to apologize. We need more people like her, not less.