<p>I'm guessing the poster on meta was taking the FAQ too literally.  What would be the point of giving the bounty owner a grace period otherwise?  Incidentally, the same thing happened to me a while ago, and the bounty was given to me by SE after the grace period ended--not by the bounty owner.  (In addition, I don't think it was right at 24 hours--maybe a couple of days later--I don't really remember.)   </p>

<p>If the OP unaccepted your answer, I'm not sure what would happen.  As I read the FAQ, the owner would lose the points, but you would not get them (at least as it stands now), because there isn't an answer with $\ge2$ upvotes.  </p>
