You're in a group of "senior" Zoners whose powers are less than a moderator but more than an ordinary registered user. That's what gains you access to those checkboxes.

Note that they're checkboxes and not radio buttons. That means you can assign a post to multiple boards--crossposting without the objectionable duplication of content.

But it opens a logical conundrum: What is the "home" board of a post when it's posted to multiple boards? What should show on that summary to the left as the post's board?

I took a first cut at the problem by recording the board to which a post is made and calling it the "home_node". In the case of your moved post, that's OT, and that's why the summary still says "Offtopic".

But I didn't think about what should happen when a post is moved and it's no longer at the "home_node"; I was focused on crossposting and adding boards to a post, which doesn't disturb its original home. This is going to be tricky, because there's no connection under the skin between those checkboxes and the "home_node" code--nobody would know to fix it when you move a post out of the home_node.

Best I can say, then, is problem noted, and I'll be thinking about a solution; but no guarantees.