Is there any reference in the song to suggest that the story behind it takes place in 1953?  Songwriter Bobbie Gentry would have been ten years old at the time, and probably not romantically interested in boys in same the way the main character in the ballad is (apparently) interested in Billy Joe.  The actress who played Bobbie Lee in the movie, Glynnis O'Connor, was nineteen at the time.  The song furthermore says nothing about her leaving home after Billy Joe's death.  As far as I can determine, the date originated in Herman Raucher's screenplay.  Raucher had also written Summer of '42 a few years before Ode to Billy Joe.  His novelization of the story was published in March 1976, during the height of the 1950s nostalgia craze in the United States, and the movie was released nationwide the following June.  The song has a 1960s sensibility about it.  I was only a child myself when the song was released, but I always imagined Billy Joe to be appreciably older than the balladeer  and consequently that he committed suicide because he feared he'd crossed an age barrier with her.