I don't think that assumption really holds up, it's very pop-history. From the Scots of the Appalachians, the religious fanatics of New England, the garguntuan influence of African-American syncretic culture, the Nordic yeoman of the mid-north-east, the southern European urban influx of the 1900s and the new, exciting Latin American syncretism: America really is a cultural melting pot. Only, really, the Virginia gentry (Jefferson, Washington, et al) can be plainly said to have imported English norms - and still, they were ideological radicals interested in forming a new nation.
The French like to call us (English, Scots, and all the varieties of American) "Anglo-Saxons," but they're hardly right. Don't give them ammo, they're already merciless!
So what would account for the difference? It must've come about after we split as a country.
I wonder if it's our Declaration of Independence including "the pursuit of Happiness". See:
Nowhere else in the world (up until then, anyway) gave as its founding commandment that being happy was an indicator of a life well-lived.Thus, perhaps, while other places reserve the effort of smiling for the emotion of irrepressible joy, Americans -- to prove they're living a good life -- present a smile.