I, as a native Chattanoogan, have no problem with the poetic license of going through the Carolinas And I do not necessarily think it implies that the train itself actually terminated in Chattanooga,
All of them, the Pelican, Tennessean and BHM Special had through sleepers from New York depending on the year
But the song says it left New York at "a quarter till four".. Well, the Birmingham Special left DC in the 3.45 or 3.50 slot for years. So a little poetic license between the two cities has always told the tale for me.
I have felt it was the BHM Special from grade school days when we would put my sister on either it or on the Pelican to go off to school in Alabama