Correct me if I'm wrong, but weren't there plenty of "message" movies
that came out before 1963???
 
Frank Capra's films of the 1930s and early 1940s immediately come to
mind.  So do Stanley Kramer's films of the 1950s and 1960s.  And what
about "High Noon"?  While this list is more than incomplete, these
were just a few glaring exceptions to your thesis that I came up with
off the top of my head.  While they were aimed mainly towards a broad
audience and did emphasize "story", their messages still came through
quite dramatically and were definitely intrinsic to the film's appeal.
 
Just a thought.