I think that information disseminating over twenty years isn't evidence of "sophisticated communication networks".
This article feels like the author is taking a few examples of Native Americans communicating, and then making no attempt to get from there to her conclusion that Natives had advanced communcation networks.
As I read it, the author didn't imply it took 20 years to decimate the information, but merely that they were well aware of who they were greeting 20 years later. Still, even 20 years can seem surprisingly short if your working assumption is that the tribes were very loosely organized and mostly isolated from one another except in a few areas.
Best I'm aware, travel speed in Middle Age Europe was ~20-40km/day. Such a high speed was in large part because a) the Romans had paved roads that were still used then to speed up troop movements, b) they had domesticated horses and cattle, and c) they had discovered and were using the wheel to cart things around.
In contrast, native Americans had only domesticated the Lama when they were around and were only using that as pack animals. (They didn't have wheels let alone carts.) And best I'm aware, the only areas with paved roads were in Central America and in the Andes.
Without all of European facilities or modern gear, I'd guess you'd probably do ~10-15km/day (if that). Aztecs had rest points on their road networks every 6-9km; doing one or two per day is a safe bet; maybe a few more if you're really in a rush.
Further, achieving such "high" speed really assumed a set purpose where you wanted to go from A to B in a reasonably amount of time for whatever reason (e.g. delivering mail or a message, moving troops, visiting someone, etc.). I sincerely doubt this was the case when it came to warning other tribes of the Europeans. Rather I'd imagine it was more of a word of mouth thing in passing, with initial groups fleeing with the information, messengers spreading the word nearby, and traders/embassies slowly spreading the word even further. That would likely slow things down even more.
Walking pace is ~3MPH. On foot people are not doing straight line trips so ~2MPH net distance for long trips is reasonable. Less if navigation is an issue. As such it's ~1000 hours to go from east to wast coast in the us.
PS: even netting 4h traveling per day that's less than 9 months.
~3mph assumes modern equipment and infrastructure. You won't get that with poorly designed shoes, a poorly designed backpack, on a barely beaten trail, and without a grocery store with (very) cheap food at every other street corner. And even if you imagined all of that, it's only less than 9 months when you're goal driven: you'd want to get a message from the east coast to the west coast - fast. Without such a goal, you're just looking at the spread of hearsay through word of mouth - which is slow.
Don't forget hunter gatherers had minimal equipment all it takes is for someone to decide to follow the setting sun and they can make the trip. Water and mountains are the major issues not so much food.
Aside from long range information, which was pretty much transferred by people (on foot or on horses), I find smoke and flag signalling very interesting. The latter could be used to convey quite a bit of information in a short time at a respectable distance...
This article feels like the author is taking a few examples of Native Americans communicating, and then making no attempt to get from there to her conclusion that Natives had advanced communcation networks.