Can an outlet for a dishwasher be located below the floor?
You are correct, the issue here is the cord and plug for the dishwasher running through the floor.  


  400.8 Uses Not Permitted. Unless specifically permitted
  in 400.7, flexible cords and cables shall not be used for the
  following: 
  ...
  (2) Where run through holes in walls, structural ceilings,
  suspended ceilings, dropped ceilings, or floors


Running the cord inside the cabinetry does not break this rule.  

Contrary to other answers, in my opinion, the cord and plug connection for the dishwasher is perfectly fine and makes it easy to disconnect power.