As of April 1, 2016, AMEs cannot issue the combined FAA Medical Certificate and Student Pilot Certificate.
Student Pilots must have a separate Student Pilot Certificate and a separate FAA Medical Certificate.
Well, I did not know that had changed. Back 28 plus years ago when involved in GA training there were a few who despite having attended a FAA physical were eventually found to be quite
unsuitable. One guy who could not pass the Private ended up physically fighting the Designated Examiner during a repeat check ride. Another arrested for attempted date rape of female student. Turned out he got kicked out of a different school for similar.
https://www.faa.gov/other_visit/avia...0shown%20below.