The article is mixing evidence for bottlenecks at different times. Your quote ...
> Because once in our history, the world-wide population of human beings skidded so sharply we were down to roughly a thousand reproductive adults.
... links to Hawks et al. (2000), with this in the abstract ...
> It is our conclusion that, at the moment, genetic data cannot disprove a simple model of exponential population growth following a bottleneck 2 MYA at the origin of our lineage and extending through the Pleistocene. Archaeological and paleontological data indicate that this model is too oversimplified to be an accurate reflection of detailed population history, and therefore we find that genetic data lack the resolution to validly reflect many details of Pleistocene human population change. However, there is one detail that these data are sufficient to address. Both genetic and anthropological data are incompatible with the hypothesis of a recent population size bottleneck. Such an event would be expected to leave a significant mark across numerous genetic loci and observable anatomical traits, but while some subsets of data are compatible with a recent population size bottleneck, there is no consistently expressed effect that can be found across the range where it should appear, and this absence disproves the hypothesis.
So yes, according to that study, the rest of the article is bullshit. But then, it was published in 2000.