Again, if a juglans regia tree is grown in California, it would be American, even though there is no such species as American Walnut, as far as botanists are concerned. Juglans Regia grown in France is called French Walnut, and when the same species is grown in Turkey, it is called Turkish Walnut. The same species (juglans regia) is also called English, Circassian, Carpathian, and Persian too.
I recently cut up an English Walnut tree for gunstock blanks that I know was grown from English Walnut (juglans regia) seeds that were brought to Pennsylvania from California. It is an American walnut tree, but it is not native to North America.
American walnut certainly is any species of walnut grown in America, and that would have to include South America as well. Canadians are Americans, and so are Brazilians. That isn't attempting to "have it both ways." It isn't hard to understand, but it is hard to convince you if you refuse to understand.