Oh? Well premium publishers have the same otpions to place ads on ALL their websites that normal publishers do. But to get the invitation they would have to own a site that meets the all criteria, so the site that got them the premium status may not have been the one you saw, but another site altogether.
Not every publishers links all their own sites to each other. Some keep their sites and registrations totally separate, so one publisher might own 3 or 4 businesses, and each site can be registered to that business independently of the other sites with no correlation whatsoever except perhaps the pub ID. For all I know, premium publishers might be given separate pub IDs for each site they own.
AdSense doesn't release very much information about the premium program so unless you are a premium publisher, there's not much detail available on how the accounts work. And, premium publishers are required to sign a NDA (non-disclosure agreement), meaning they can't tell anyone else how it works, or in fact anything at all about how they got the invitation.
Not only that, there are hundreds of publishers who attempt to modify their ads to resemble premium ads, because they think they can. Anyone could mistake a site who has ads that look premium as a premium publisher, but those sites will eventually be disabled because we aren't allowed to edit the ad formats. Lots of people think they can use certain ad formats because they see them on other sites.