I'm not too sure the article is for real -- last year the drumbeat was, not enough African DNA, where's my African DNA, racists racists racists, along with where's my Native American DNA etc. More people are getting their minds around the idea that the family stories about Precolumbian tribal roots were actually about African roots, and that African roots can't stay that way if the white devil slavemasters you've been complaining about were studding all their slave women.
The main thing is, people don't seem to realize that they only got half of each parent's chromosomes, and since there are 23 pair, iow, not evenly divided by 2, their DNA is coming at least slightly disproportionately from two of the grandparents (one on each side, or in some families, well, heh), and that skew continues, because we really have 46 family trees. By the 6th-great-grand generation, there are 64 names, but at most (again, assuming no family crossroads on the way back to that level) only 46 managed to squirt any of their DNA through.
Sunk, I think you're making a classic mistake. Yes, there are 23, which you correctly point out is not evenly divisible by two, but it's 23 PAIRS—with one of the pairs comes from the male gamete and one from the female gamete—making a total of 46 genes. i.e., there are TWO sides to each of the 23 chromosomes and each can be traced, and 46 can be divided by two.
Take a look at the limitation of DNA testing they really use as I laid it out to dila813 above. She's not interested in facts, but I know you are.
That being said, one other thing being missed here, perhaps not by you, but by everyone else, is that many families assume that everyone in their family tree was faithful to their spouse of record and the children born of that union were actually the result of only those two people. One of the results of modern DNA testing was the discovery that is not true.
Amazingly the percentage of children born in seemingly solid marriages that are NOT the child of the husband of the mother of record is amazingly high. . . several DNA studies put it at 1 in 10 children were fathered by a man not the husband. (some attempts have been made to debunk that based on extremely small populations that put the percentage at 1% to 2%, but these were historic studies, some several generations back, based in statistical analysis reaching the conclusion that past generations were more faithful in their marriages than current married couples or, alternately, pregnancy prevention in the past was more effective or abortion was more frequently used to end an out-of-wedlock pregnancy that resulted from an affair.)
As one goes farther back in time, and assumes a similar discrepancy rate for family tree wolves in the sheepfold, the possibilities that someone from from an unknown source outside the known lineage contributed DNA approaches 100%.
My family tree on my mother's side and my paternal grandmothers side can be traced back to the Domesday book with supposed accuracy. There's royal blood in there, one of my Great-great-grandfathers was Alexander Graham Bell on my mother's side, the first English governor of Massachusetts, somewhere George Lucas and I share great great grandparents. way back Daniel Boone makes an appearance. . . and on my father's side, Kit Carson (my father's middle name of Carson comes from that relationship). . . but we know there are bastards in the mix as well who don't have a clue who their fathers, and sometimes their mothers were. I know that one great great grand mother was Cherokee. . . "rescued" from the heathens as a child and raised to be "white" and married into the family without a clue about her parentage except it was Indian. Farther back than that is impossible to know. That's a huge wolf in the woodpile.
On my father's side, one ancestor claimed to be the Lost Dauphine of France. . . and had proof. But that and $7 will get one a cup of fancy coffee at Starbucks. It's sorta like all the Anastasia's who've come out of the woodwork after the 1920s to claim the Russian crown.