I ran into the same issue in Safari, caused by the Stack Exchange global network auto-login using HTML5 local storage. Safari does not show that, but also does not allow me to delete it.
Browsing to stackauth.com and pasting the following into the location bar, shows it:
In Google Chrome "Delete cookies and other site data" also clears local storage. In Firefox, it's deleted whenever cookies are deleted. In Safari (on a Mac): no luck, other than deleting directly from the file system (
~/Library/Safari/LocalStorage on my Mac, which incidentially shows all domains that use local storage one has ever visited,
including those not using local storage at all, even when using private browsing).
(See also How to clear all HTML5 local storage from Safari? on Super User, Global Network Auto-Login on the blog, and Kevin's detailed explanation in How does SO's new auto-login feature work? here on Meta.)