I agree. African-American is American culture. This isn't a foreign land to us, as it is to Asians. AA have been here since the beginning.
I think it's hard for people to say African-American culture is American culture, like you said, because Blacks want to keep what is theirs, theirs. I even feel this way. Everyone seems to benefiting more from the culture than Afrian-Americans, who have helped to shape it.
It makes me mad an Asian can come over here, in a Black community, and make mad loot off of Blacks with their African-American hair care shops and such, but a Black person can barely keep anything open in the Black community (at least that's how it is where I live).