"I don't believe places like Texas, Oklahoma and Nebraska qualify as "the South."
Nebraska is Midwest, but Oklahoma is considered "American South" and Texas is DEFINITELY "South" (as opposed to the "Southwest"). Perhaps you're thinking of "Deep South" (of which East Texas is often included)?"
As a Tennessee native, I (and most people around here with whom I have discussed the subject) do not even include Texas when defining the South (Southwest seems more accurate- it's a different culture in addition to the geographic differences) and definitely don't include Oklahoma, which I would argue is a Midwestern state.