To your point, yes, there are plenty of journals that don't pay (but pay for other activities). Perhaps I should have just called it a fee instead of a job. Here are some that do pay -
http://academia.stackexchange.com/questions/20930/
Interesting link! I wasn't aware of anyone paying for peer review when I was in academia. It appears from the linked examples that it's still rare and relatively small dollar amounts, so indeed not a job.
I love the example of the New England Journal of Medicine finding that paying $5 was worse than not paying, as potential reviewers found it insulting.
As to other activities, yes, I think companies behind journals typically pay people to do administrative functions for the journal, and the editor may or may not be paid (for Nature, I believe the editor is paid). However, it is possible to replicate the traditional review structure in a completely free OA journal with volunteered resources; in computer graphics, I think JCGT does this: http://jcgt.org/about.html