737s probably aren't too good at playing Red Air... I imagine they were using the Skyhawk to provide DACT, simulating something from a little further east.
frodo,
Maneuvering against an aircraft with the renown, but outdated capabilities of the A-4 is RTU level stuff. (We had F-5 & A-4 adversaries for F-16 RTU in the 80s, as well as Eagle targets)
If you get to the Weapons School without already being able to kill a MiG-17 with an F-16, F-22 or F-35, I 'spect you missed something earlier and know somebody or have pictures.
One would suspect, the 'PhD in flying' involves more gizmo awareness and less 'turn & burn'. 737 can carry a whole bunch of gizmos. Call them Jade Air.