The Int'l syllabus has both a Natural and a Reverse basic step, meaning that you can start with either foot. Of course Corky and Shirley weren't "wrong" (Would I ever dare contradict them?) -- they simply chose one of two options, their own preference.
I haven't seen a Natural basic in any of the American style syllabi that I've worked with (AM, FA, Terpsichore), so I would generally expect to start with my left foot in American or social style here in the U.S... unless I was dancing with a lady who was trained primarily or exclusively in Int'l style, and then it would depend on the preference of her coach or teacher.
That being said, let me make things really easy on you with a quick tip: If you find yourself in a situation where there is some question as to which foot she's accustomed to starting with, you can always ask. Or you can begin standing on one foot with the other foot pointing sideways. She'll usually notice and position herself likewise. If not, do a weight shift or two to give her the message. Movement to the side will synchronize just about anybody.
Sincerely,
Jonathan Atkinson