"I don't think so" vs. "I think not"

I've recently been told that "I don't think so" is, in the U.S.A., a southernism, whereas "I think not" is considered more acceptable everywhere else. Is this true?

Example:

Q: Is your wrist broken?
A: I don't think so. / I think not.

I think not! In British English, I don't think so. and I think not. are both used, although they have different nuances.

I don't think so. is more common, and shows a little diffidence or uncertainty.

A: Is it going to rain today?

B: I don't think so. I'd just wear a t-shirt if I were you.

I think not. is used to disagree emphatically.

A: You still owe me.

B: I think not! If I hear any more from you about this, you'll be hearing from my solicitor.

Sorry, but I don't have any references I can cite. Just my personal experience.

I think not is a formal way of saying no. It's often used in parody, faux and overly dramatic situations, to heighten the negation and introduce a sense of inadequacy, foolishness and insignificance.