Was there a dedicated desk before? That was always my understanding, but taking a closer look at the website (below), I guess it only says that we have a dedicated phone number to call and that we will have priority over other calls.

VIP PHONE LINEYou receive access to an exclusive VIP phone line dedicated just to our Diamond Medallion Members and you'll receive handling priority above all other Members.(11) You can find the Diamond-only phone number when you login to the Fly Delta app under “Contact Us” or on the back of your Diamond Medallion card.