Personally I'd be worried if I were you. Credit scores are important for everybody, but they are particularly important for people like us that like to play this game ( miles, points, Credit cards, Etc.)
It is certainly possible that they are bluffing and do not have the intention or capability to report to the big three American credit bureaus…But if they are not bluffing, and they actually follow through on that threat, then you are in big trouble.