Apparently the rules for admittance are quite fluid. The Delta rep at the desk in T4 made a phone call and said I couldn't get in unless I was traveling in international business class. Undeterred I walked over and was admitted without delay. I'm traveling from JFK to SAN in X class. No international itinerary. I really like the hot and cold food options and self service bar.

I couldn't get in upon arrival yesterday from SAN, so I called the Diamond desk. Was told that even Sky Clubs won't admit passengers upon arrival, which is completely false. Hung up in disgust of the lack of knowledge of their own product.