I believe Stack Overflow uses Web Storage to locally store login preferences, and your OpenID/OAuth provider might be doing that as well. If you’ve enabled the Develop menu (Preferences > Advanced > Show Develop menu in menu bar), you can fire the Web Inspector (Develop > Show Web Inspector) and select Resources > Local Storage to inspect what has been locally stored by stackoverflow.com (in my case, meta.stackoverflow.com has stored a key-value pair with key
I also believe you’re using and ‘old’ version of Safari. Version 5.1.1 (7534.51.22), when asked to reset Safari, shows a ‘Remove all website data’ option as the last checkbox whilst your screenshot doesn’t list that option. If I select that checkbox when resetting Safari, I need to log on to Stack Overflow again, so it certainly removes Web storage.
You should also be able to remove local storage with Preferences > Privacy > Remove All Website Data…, at least on Safari 5.1.1. Furthermore, the Details… button shows how a given Web site is using local data: cache, cookies or local (Web) storage.