From what I have seen, the CK staff seems to be based largley out of the Admiral's Clubs (or Flagship if one exists). Having spend a good part of my life in the LGA club (and personally knowing the CK rep), it appears that most CK transactions are handled by the club staff or the CK rep themselves. It also appears that they can at times (IRROPS) override just about everything (i.e. Book the CKs directly onto a "sold-out" flight, jump the upgrade list, etc.