Interesting. If it is as you describe, maybe the way we were taught was purely a simplification of the actual theory.
I did take a look at "Aerodynamics for Naval Aviators". On page 94 (while referencing a chart on page 93), it states "The point of minimum total drag occurs at a speed of 163 knots. Since this speed incurs the least total drag for lift-equal-weight flight, the airplane is operating at (L/D)max", which would contradict you statement.