I think Wolfgang's "A Slightly Different Story" means that ANY New York racetrack would have been considered "the Big Apple" not one particular one. Since horses like apples as a food treat I'm guessing "the Big Apple" was considered the best treat of all (i.e. racing on a track in New York). I don't know much about horse racing (except that occasionally I've won a few bucks betting on the right one!) but perhaps when the term was coined New York was considered the mecca of horseracing.