I'm always wondering about these claims of population: how would we know all the structures were active at once? Perhaps its a century of building, with structures abandoned as they decayed and new ones built. Then the population at any one time could have been at most a percentage of the estimates.
In this case there is circumstantial evidence - from what I understand there is a huge difference in population estimates between the first time contact was made with Europeans, and every time after that. All accounts point to an apocalypse due to diseases, even before the Spanish conquistadors came.
In other words: it was the previous ground research that was at odds with the written accounts.