The assumption that he puts forth is that between the first explorers, and the large wave that followed later, there was a massive death rate due to the introductions of Western diseases. This large die-off was not seen or recorded, by Westerners, because the bulk of it occurred between the exploration stages.
He discusses many of the records of the second wave of explorers, they wrote of well tended, but empty, forests and fruit plantations. Many of their observations reflected that there was a recent, and large population; yet they were not seeing that large population. here is the wikipedia summary https://en.wikipedia.org/wiki/...
The, essential, anarchy seen by later explorers, and settlers as not a fair look at how the Americas had been. What those of the later stages were seeing was the result of a societal collapse to below the levels need for continuation.
To put this in geek terms, imagine that you arrived on earth after the zombie apocalypse, your assumptions would be different than they would be if you arrived today.