I felt ignorant first when reading it as well. But looking at the "FAQ" at the bottom, it says:

"But this only affects people that are logged in, right? Yes ..."

So I suppose what happens is, that the user is already logged into the service and thus has a cookie for the service in his browser.

If the user then somehow executes a request to the URL in the article with the same browser (eg viewing a malicous email with the IMG tag in a webmail client), the browser will enclose the cookie in the header of the request. This makes the request automatically authenticated.