Oh, I've finally managed to do it, but it took way more effort than it should have, and I know that someone like my mom wouldn't be able to do it at all.
Not interacting with Facebook sounds easy, but it's not.
You have to clear the caches on every browser on any computer that you've ever logged into Facebook with. You have to delete all native Facebook clients. You can't log into any site that uses Facebook Connect. You can't accidentally click on a Facebook 'like' button. You can't respond to any mails Facebook sends you or click on a Facebook related link. Etc etc.
If you so much as look in the direction of Facebook during the two weeks following your deletion request, it is canceled.