Can't any agent answer the queue of calls and when the customer's information populates it shows that the customer is a DIamond or Medallion Member and address them as such? As long as the agent is logged in they can get any calls even priority calls from the Frequent Flier Priority Line. Perhaps this agent was not trained or was a new trainee and sadly you got the brunt end of it.
I would have asked for a supervisor and if the agent refused I would ask for their Agent# and document the date and time of the call and call back or Tweet Delta for them to pull the call and listen to it. Perhaps Delta had issues with this particular agent and is building up a case for either reassignment or dismissal from Delta. Delta needs to hear about this and yes they do record and monitor the calls for quality and training purposes. Perhaps this agent's supervisor was listening in on the call but I would still report it.