I would try it out with a test user just to be sure, but I believe write, create, and delete rights would do it. Or admin would definitely do it.
Bear in mind that you have to trust your publishers, because edit-this-page trusts the publishers. Since they have control of HTML content on your website, they can easily hack it if they know what they're doing.
Thanks, Jade. Seems it works. They won't hack the website (1. because they are nice, 2. because they don't know) unless it could happen by chance. Could it?