Thanks for clearing up the terminology.
I am surprised that this was not clear from the quote; perhaps it's a matter of giving the benefit of the doubt to the user vs the moderator?
I think, if the parent had included something like "and therefore I am deleting your post," I probably would not have been confused.
You think you're confused? Apparently when my comment was deleted by a moderator, it is NOT deleted in my own view of the thread! So I am reading these confused followup comments with people talking about my having deleted my comment, and I'm staring at the page SEEING my comment there! It was only in a different view where I saw my alread-deleted comment did not have a "delete" option on it while a newer retracted comment I had made did show a delete option that I guessed that my comment had been deleted, but with no indication on my screen that it was not publicly visible.
http://www.quickmeme.com/Overcoming-bias-guy/popular/1/?upcoming