It is not American culture but Western culture that IS superior to all others. It is the continuation of what began with the ancient Greeks, rationality, logic, human achievement, observing the world around you instead of looking to the supernatural.
In the 18th, 19th and early 20th century no country on Earth represented Western culture better then the USA. The more the USA falls prey to multiculturalism, social democracy, religious fundamentalism and regulation of private enterprise the darker the USA becomes and the greatest beacon of the Enlightenment dims.