The bigger issue, for me, is that I'm not sure how they can rule out the possibility that there were lots of other people around at that time whose lineages gradually died out. Modern genetic lineages may trace back to 1280 people (+/- the margin of error), but it seems pretty dubious to assume that those were the only people living at that time. It seems highly likely to me that there were infertile people, people who died young, people whose only living children were infertile or died young, etc.
(I did not read the original paper, so maybe they accounted for this, or maybe they that specify that this was a genetic bottle neck for modern humans, but not necessarily the actual size of the population.)