>scores for African-American students were the lowest, and they're obviously native speakers.
This isn't entirely true. There is a great diversity of dialects of English. Schools test and grade students on their abilities with "standard" English.
For historical and racist reasons, African American Vernacular English is considered by many to be "stupid English", which puts many African American students at a disadvantage [0].
Setting dialectal variations aside; no one speaks standard English. In fact, "standard English" (that is, "correct" written English) contains rules that are not, and have never been, part of any dialect of English that I am aware of. For example, in standard English you cannot split infinitives, and must use commas (which aren't a "thing" in spoken English) in certain places. Further, the phonology of standard (written) English is miles away from what anyone says. This result of this is that being a native speaker of English is not sufficient for anyone to learn standard English. To do so, one must be exposed to sufficient written material; and exposure to written material tends to correlate with class.
[0] Admitidally, it is true that, as far as English dialects spoken in America go, AAVE is relativly distinctive from standard English (likely due to our history of segregation).