There were two factors that, together, made this happen: first, the admin login form was implemented in JS, and if you went to log in with it with JS disabled, it wouldn't verify your credentials. And it submitted via a GET request. Second, once you were in the admin interface, you could delete content from the site by clicking on an X in the CMS. Which, as was the pattern, presented you with a JS alert() prompt before deleting the content... via a GET request.
Looking at the server logs around the time it got "hacked", you could see GoogleBot happily following all the delete links in the admin interface.