Incidentally, reddit had this exact bug almost two years ago, and spez fixed it: http://www.reddit.com/r/reddit.com/comments/6b2kq/
It happens because our ISP is caching the other guy's logged in page, and then serving it up to me (and vice versa, I suppose). I'm pretty sure my ISP's caching proxy is following the HTTP spec. HN can fix it by giving more stringent no-cache headers. At the moment HN says "Cache-Control: max-age=0". reddit serves "Cache-Control: no-cache" as well as "Pragma: no-cache" and that seems to do it.