I had started a non self-moderated thread and while viewing post history of one of the users who had posted there, I saw the option to delete that particular post :
It is not board specific, I checked with other threads that I had opened in other boards too, and the option is still there.
Although while viewing the posts on the thread there is no delete option, as one would have if the post was self moderated like this :
I haven't tried to click on that button to delete any posts, but I would like to know whether the button works or not. If yes, is it intentional by forum admin?