The last edited by... should be on a timer. If you edit your post within a set amount of time, you shouldn't see it. It appears to be more than one minute but less than five.
My gut tells me that someone you know obtained your password or used your cookie from another computer that you have logged into. A shoulder-surfer at school, a sibling at home, etc. As unlikely as it may seem to you, it is the most likely reason since if an admin/mod edits your post, even under the edit timer, it will leave a last edited by.... notice. I think.