I was listening to NPR recently while they were playing world music, mostly European, I was not able to tell it was not American. How much of that is due to immigrants bringing their music to the US and how much has to do with the exporting of US culture?

This is a very tough question to answer without knowing what specific examples you were listening to. Each culture is going to interface with American life in different ways. And each impacted american music to varying extents and in different ways. So how Polish music impacts American style is maybe a different story from how Irish Celtic music does. So without more specific details, it's hard to tell this story.