Of course America has no culture. There is no California roll sushi, only Japanese style. There are no award-winning musicals like Grease or Rent, only classical plays from Shakespeare. And everyone here says "Hello", never "Hi", "Howdy", or "Wassup".
The most telling sign that America has no culture is definitely in its children. As we all can see, every child born here retains exactly the cultural identity of his/her ancestors. That's why I'm typing this in French rather than in English.
No, we are indeed a culture of our own, made up of the best (and maybe a bit of the worst) of many cultures and then blended into something uniquely American.