Abe> Search engines gets the same HTML as guests (unless there are hacks that forwards it to archive); however, as opposed to guests, Search Engines sees it at raw source level, doesn't matter whether or not the icon is 'displayed' on screen. And it sees in the HTML there's a link, so it follows. Adding the rel="nofollow" in the a href tag tells it to not follow the link all together. I've gone ahead and added it to my forum now.
As to WHY it still clicks it, it may be a cached version of your page or something. It should stop after a while...