So have I got it right that Americans think of the hand the opposite way around from us ie, with its 'back' on the opposite side?

No, it's the same side.

Americans are just masters at slapping asses. The variations in the way we that slap asses is like a language in itself, which foreigners can only learn under the great risk of their identity dissolving into vapor, or that pink stuff Chicken McNuggets are made from.

One fine day, perhaps, Britons will learn to slap asses in the back-handed way. They'll dub it "The American way," just to be clear. Part of the population will rush to do it that way just because it is the American way. The trend will spread from Liverpool, whose fake-tanned population will embrace it with a will, while Southern urbanites will disparage it. But it will finally spread to the communities outside London, and even the old country geezers will take notice. News outlets will deem it a "chav" thing, and others will use its example rhetorically to express their on-going bitterness (or, "butthurtness," in America-speak) over the fact that American ways have spread in the world, and Chinese students are not putting a "u" in the word "color."