We do not know that the cashier’s assumption of his Americanness was based entirely on what she perceived to be his race. What is probably most true is that her mind, based on a large dataset, “guessed” his Americanness and that his race may have had as much to do with that guess as his shoes (probably wearing sneakers, as American tourists tend to), his hat, glasses, shorts, phone, etc. Ever been to Europe as a white male American? They can tell you apart from white male Europeans instantly (usually from your shoes).

Edit: words and grammar.