Not familiar with the "delete" button they're talking about. However, you can delete all the content even if you can't remove the thread itself.
Just go to the original post, as long as its yours, and click the "Modify" or "Edit" button. Then delete everything in the text box, and click the button that submits the modification. Presto chango, all the content of your original post is gone. You have to do the same for each additional post you made to that thread, and you cannot delete the content of any replies, but it is one way to do what you're asking about.
Of course, the next level is to ask Harry P or Gregg to delete the entire thread.
Hope this helps.
Ahhh! There is a little "delete" button down there.
I'll check it to see what it does.