Rather than suggesting that people delete their cookies, you could suggest checking the article in private browsing mode (or whatever their browser of choice calls the feature).
Google has invented a new login state between "logged in" and "not logged in" called "not logged in enough". It's kind of like being logged in, except nothing works and you get asked to login again. Also, you can't logout.
Delete your cookie or sign out. It's just a Google Groups thing for you to refresh your session and I dunno, parallel login or something (they may never have completed the dejanews cutover). Unknown users don't get a login prompt.