[roughly]

It's not an exaggeration.

As the other response notes, Tenochtitlan was possibly the largest city in the world at the time, and the Aztec empire contained many other cities with populations over 10k. The Inca built a massive empire (8-12M people) centered on the Andean mountains linked together by roads and suspension bridges and built monumental architecture using masonry techniques that are impressive even today. We're just starting to get a handle on the scale of the Mayan empire, because they built their cities in parts of the Guatemalan jungle we have a hard time getting through today - some of the more recent work has found evidence of raised causeway networks stretching over a hundred miles linking large scale settlements. Go further south, and the Amazon jungle basin has been considered uninhabitable because of the density of the jungle and the poor quality of the soil, except that we've found evidence of cultivation of plants and more recent evidence of large-scale settlements and waterworks.

The Spaniards did not walk into a backwards people or somehow just miss what they were looking at - the civilizations and cities they found were advanced and obviously developed and on a scale that, even outside Tenochtitlan, would have rivaled European cities at the time for both size and sophistication.