My exact words, from this article, were: "The western arguably constitutes America’s single most outstanding contribution to world cinema." I stand by that statement, and in retrospect would like to remove the "arguably". Westerns are a uniquely American genre, as you say, in that they constitute a form of American mythology. And yes - there really aren't any westerns in other cultures, although the genre can replicate itself to a degree in vast and open spaces (for instance, I'd argue The Proposition is an Australian "western").
To quote The Man Who Shot Liberty Valance: "Print the legend."