How do pilots and controllers deal with TFR's that lie directly on an approach?
The NOTAM itself answers your question:


  THE RESTRICTIONS DESCRIBED ABOVE DO NOT APPLY TO THOSE AIRCRAFT
  AUTHORIZED BY AND IN CONTACT WITH ATC FOR OPERATIONAL OR SAFETY OF
  FLIGHT PURPOSES, DEPARTMENT OF DEFENSE, LAW ENFORCEMENT, AND AIR
  AMBULANCE FLIGHT OPERATIONS.


As long as the pilot is in contact with Air Traffic Control and has been cleared through the TFR, they can safely fly though the airspace.