True, to a degree. But there is an African-American culture. Just like there is an overall European-American culture. It's just that the European-American culture is more commonly referred to as "American Culture" in general.
There are various white sub-cultures as well. Southern culture, Midwestern culture, east coast culture, west coast culture, Southwest culture, etc.
They are almost always geographically based for the various white sub cultures.
African American culture, though, tends to be more universalized and is often an amalgamation between older slave traditions, southern traditions and more modern traditions.
If you want to discuss stereotype then that's a completely different subject - there's no rule that dictates what "race" is connected with a particular "culture"
Actually, Garth Brooks would probably spring to the minds of many people in Ireland when you say American Culture. They wouldn't really think of James Hetfield, but country singers are often the basis for American stereotypes as of late.
Especially when talking about "Proud to be an American. That almost immediately causes people to think of country singers.