Finding no selection in African-Americans over 300 years is not evidence against selection: five generations is simply too short a time to compound.

And so one possible explanation for that is just that there's only a handful of generations maybe five over which the natural selection would operate. And so maybe if the selection was 2% a generation you would still only see maybe a 10% compounded effect and there's just not enough time to detect it. But the Bronze Age is not 300 years, it's 3,000 years. It's the power of compound interest and you have enough time to begin to see a strong effect.