I'm not sure exactly what those quotes are referring to, but many reports of European settlers to the New World, while technically true, were greatly misleading.
Prior to arrival of the Europeans, the continent was full of Native Americans who lived in an ecological balance with wildlife.
When the Europeans arrived, the diseases they brought wiped out 90+% of the indigenous population, according to some estimates. By the time they explored the continent, the population was mainly gone, far in advance.
So there's a strong theory that the incredible over-abundance of wildlife the Europeans saw was actually a huge ecological imbalance, as many animals had lost their natural (human) predators.
And that phenomena such as millions of passenger pigeons blocking out the sun overhead weren't "natural" at all, but actually severe ecological imbalance.
(This isn't to say, of course, that now we haven't swung way too far in the other direction. But just that the tales of abundance aren't necessarily a naturally balanced state either.)