Treating "black-headed peoples" as a ethnic designator is a bit of a blind alley because there is such thin evidence on the question of whether or not the peoples of Mesopotamia ever saw "Sumerians" as a distinct ethnic group, or even on the question of whether the modern conception of ethnicity had any real salience in Mesopotamia(it's not clear that people actually said "I am Sumerian" from the textual record), that attempting to extrapolate some kind of Sumerian Race has been quite rejected as a project. It seems clearer from the textual evidence that the salient distinction is between people of the city and dependent countryside and people of the wilderness and steppe, or to put it another way between the desert and the sown. What is meant by "black-headed people" here remains obscure. Herman Vanstiphout suggest very interestingly that it is a indirect reference to sheep(often black-headed), invoking the image of the king as shepherd.