I think there are two mostly separate issues involved:
1. Were the woman's actions in returning the watch particularly praiseworthy?
Returning the watch was the only ethical and decent thing to do. On the other hand, there are a lot of ethically-challenged people in the world, and I imagine it would have been hard to track down the culprit if the watch was taken out of the venue, so her actions do suggest that she is a genuinely honest person, not just someone who's honest when people are "watching".
2. Did Chris Brown have an obligation (either morally or by etiquette) go out of his way to thank her?
IMO, he should have. I could understand not going to a lot of trouble to thank her (bringing her backstage, offering free tickets, etc.) for an item of little value (e.g. if he lost a water bottle or something). However, when (general) you are careless with your belongings, especially valuable belongings, so that strangers have to go to the trouble of taking care of your belongings and returning them to you, then I think you owe them a decent thank you. I think tossing an expensive watch offstage (whether it lands backstage or in the crowd) is being pretty darn careless, and I think he should have made a little more effort to at least thank the fan in person.
ETA: Part of my reasoning is that I think the amount of effort someone puts into returning an object is likely to be related to its apparent value. If a performer accidentally kicked his plastic water bottle off of the stage, I'd consider it enough to pick it up and set it somewhere where it wouldn't be stepped on and could be retrieved later. But if the lost item was expensive (like this watch), had obvious sentimental value (e.g. a cheap plastic water bottle that had been decorated by a child), or if I was told that a lost item had sentimental value (e.g. they announced that Performer X's favorite "lucky" water bottle had been knocked into the crowd), then I would feel a much greater obligation to make sure that the item got back to it's owner safely, even if that meant missing part of the performance/staying after the performance ended/etc. So even if Chris Brown doesn't consider that watch to be an enormous expense, his carelessness put a stranger in the position of having to make sure his property got returned to him, and that deserves a thank you.