Should a copy editor only edit copy?

In a nutshell, no. A copy editor also needs to think about the content of what they read, and look for inconsistencies or inaccuracies. Often, I find problems with text that my client missed entirely, and even if they hire me simply to tidy language, I always feel it's part of my job to flag up other stuff that jumps out at me. So although 'All women hate chocolate' is grammatically fine, I'd still be writing a note for this sentence that says something along the lines of 'Really? Are you sure? Is this a fact?'