I don't know why so many people make the point that hierarchical structures are how the brain works. Graphical structures are how the brain works. The hierarchical structure is how the physical world works (you can't put the same shirt in two closets), and we have an unfortunate habit of trying to force our brain to work the same way, but it's an impedance mismatch. Unless I'm the only one that is frustrated that you…
Regarding non-hierarchical information organization however, keep in mind that this article was only a very quick intro to the most basic possibilities of org-mode.
Org-mode actually provides a pretty powerful set of non-hierarchical structuring functionalities by using tags.
Within org-mode you can add arbitrary tags to your items, you can define custom sets of tags for auto-completion, you can get a filtered view based on a tag search across multiple documents and so on (see for example http://sachachua.com/blog/2008/01/tagging-in-org-plus-bonus-...).
In addition to tags, org-mod provides a second similar mechanism with properties (searchable key/value pairs annotations to your items).
So org-mode definitely does not restrict you to a hierarchical organization. It is a very cool tool box that, coupled with the programmability of emacs, offers a lot of flexibility to adapt to your own way to do things.