That's technically correct too. But it still remains that the services are there to support a population. Housing will always vastly outnumber religious, governmental, or business systems. There is a statistical number for that, though I don't remember it anymore.
Even if that number knocks off 30% it is STILL reasonable to claim that the LIDAR sweeps on either side of this one will have a similar density. No matter what you do, that's gonna be a butt-ton of people.
That's gonna require networks to sustain. It has to.
My guess is that those networks were not evident at the scale of the LIDAR scans, or simply not in the surveyed areas. Romans built great roads, and parts of those survive today. Their engineers built aqueducts that still carry water, and their mastery of concrete by accident or design still has eluded modern builders until recently. Incredible engineering and execution.
But the quality and durability of a road is commonly a factor of available materials, and those may not have been such that the roadbeds would have survived being uprooted by jungle and ordinary erosion. Canal systems, much like flumes used to carry water to mines in the drier parts of the American West, may or may not have survived.
The only way to know is to get there and dig, but I'd want more thorough and comprehensive scans of the area with the highest resolution available first, just to pick and choose sites.
Keep in mind that we just don't know what wiped these people out, and that is a mystery that itches to be solved, despite blaming European Pathogens for the reduction in numbers of the native populations. (In some cases, in North America, correctly so, whether by accident or design). In the same vein, plant pathogens affecting specialized crops or trees that yield food could collapse a society, too, as vital food sources die off.
Keep in mind that the workers cities for building the Egyptian pyramids are only now being uncovered, as Archaeology has reached the tipping point from treasure hunting to understanding the dynamics of ancient societies (and what led to their fall), and the agricultural support mechanisms for large populations may not be evident.
How much of their agriculture was tree based and animal husbandry, we don't know (they didn't have our food pyramid and a bias toward cereal grains, as far as we know), and vertical (tree based) agriculture might produce more food in a smaller space, although preservation (drying, fermentation, packing in honey?) might be problematical. Nuts would have fewer problems. And all of that depends on the climate at the time of occupation, which may have been considerably different from today.
What may or may not have been orchards organized as we would do, would become disorganized over a few hundred years in the wild, with trees seeding their own successors to the point that in a few unmaintained generations the distribution would become more chaotic and not give the appearance of being rooted (pun intended) in human endeavour.
Only botanical surveys for food producing plant distributions might answer that. Building materials might have been cultivated as well, but while LIDAR may provide evidence of habitation (not necessarily simultaneous, just extensive) it can't answer the questions of food production--it sees through the very vegetation that would need to be studied, both living and any seed or pollen remnants from the past.
I don't think those agricultural ideas are new, just rediscovered.
As for sweeps adjacent to the current data having the same distribution of structures, maybe not. In the American West, for instance, some north to south or east to west sweeps would disclose centers of high populations, (Say, along I -94) but a sweep north or south of a sweep of I-94 would yield relatively little in habitation evidence, those being agricultural areas that support (in part) the communities along that thoroughfare. Spectacular results are more likely to yield the sort of funding that can lead to more research; boring (for many) images of what were huge garden plots just don't prod the imagination the same way.
One thing for certain, the scans raise more questions than they answer.
