In practice, unless you are going to look specifically for it, Kraft, Velveeta et. al. are more than happy to sell you "American cheese product" which does not meet FDA standards for labeling for American cheese, and in practice a lot of people criticizing American cheese are actually criticizing cheese product, which is what is super easy to find both in American supermarkets and abroad.
Europeans also generally take offense at some of the stuff in American supermarkets that has implied labeling like European cheese, like the powdered Kraft Parmesan.