Copyright is automatic where it is automatic. In the United States you don't need a copyright statement. Also, no matter where you're from, "all rights reserved" is meaningless (post-Berne Convention).
It's (as I understand it) legally meaningless, but it's not "meaningless": it's a socially acceptable way to express the sentiment of "this is not open source or in any way something I am sharing with the public". Avoiding confusion is a good thing. It's like the opposite of a GPL COPYING file.