To be more precise in a few more words, the article makes two points:

* some papers rely on McEvedy and Jones’ Atlas of World Population History data as the ground truth, when a lot of it is the best educated guess (sometimes the guess is based on basically almost nothing).

* the difference between the "guessed" population and the real population (which do not observe) is not random, which would lead not only to less precise results but also to bias.