That information has not been updated on that page for quite some time. Clicking the "Private Beta" icon doesn't do anything, it never has, it's just a tile there for show.
For any issues with the Xbox 360 Dashboard Beta please make a post in the private beta forums here.
If you're getting "GROUP NOT FOUND" when visiting the page above then this means that you don't have access yet. Please be patient as a forum support staffer will need to check if you're eligible for forum access. You can only access the beta forums
from the gamertag that actually registered for the beta dashboard. You will not be able to access the private beta forums if you've downloaded your profile to another console and that converted your account from points to currency.
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