I remember learning the American Swing over twenty (20) years ago at one of the first RKC's. Back then it was called the "Two-hand Snatch", because that's what it boils down to. The trajectory of the Kettlebell matches that of the High Pull, Clean and Snatch.
It has absolutely no relation to the Swing, unless you learn how to use Kettlebells from another gym that is. Seriously, you don't want to be stopping the KB overhead with your shoulders. Just let gravity do it's job and you'll save some serious wear and tear on your shoulders.