if you make the file deletable, the folder containing it must still be writable.
Only root can do certain items like change a user etc.., and php is running as either apache or nobody.
One thing you might consider searching on is to run php as a command line file. Create a file that will accept the switch for the file name(s), and also have a switch for a password. Then make the file executable only, and call this file (from a normal .php page) with the password and file name(s). The file doesnt' have to be readable to work, so the matching password need not be stored in visible format.
Since the file belongs to root, it will have root permissions, and can do what you're asking -- kind of like sending in your older brother, but in this case a limited older brother for a specific task.
BTW I've never done this but I know it works, I will need to implement this on my server myself at one time.
Sam