I cant say with 100% certainty, but my experience so far has been those ranks work for public leagues but not for private. I am able to see my player list but not rankings for all teams using the top link, and my draft rank for public leagues but not private using the second link.
That's it. I only play keeper leagues these days which are private. But I went back to an old Autoleague team and the second link above took me to the "Rank your players" page. Thanks for clearing it up Chris.