I'm logged into Area51, and can see which sites I'm a part of. All good and well, but when I go onto the page of a site that is in private beta, I still see the button inviting me to visit the site. Of course, once I do so I see a page telling me to come back when the site goes into public beta.
If you know which sites I am committed to/following/active in private beta, etc. then why not use that information to hide a private beta button?