I read somewhere that using african american is also bad since there are many black people that don't identify as african and don't even have african heritage. I think black is much more inclusive.
African-American also has the problem that not all black people identify themselves as American. Although it does lead to an interesting conversation about American imperialism when one expresses concern over how much of African governments are run by African-Americans.
Also, there are plenty of non-black people who were born in Africa.