Those explorers found, for example, that they could wade right in among thousands of nesting birds and just grab dinner from the nests at their feet, either by clubbing a bird and/or by stealing its eggs.
Check your sources again. I bet you'll find that the hunter's paradise described by these explorers were in places that lacked in predators of all kinds. It wasn't that the Dodo Birds were not afraid of men, but that they weren't afraid of anything. The passenger pigeon only became vulnerable because of the technology to kill them in vast numbers wasn't available before the stone-age nomads were supplanted.
But you are thinking of hunting and gathering today, long after hunting pressures from overpopulation made harvesting directly from nature impracticable.
Hunting pressures derive from the total population of predators, not just the humans. If there is an abundant supply of game in a given area, the population of predators rise until there is no longer abundant game. Look up what is occuring in the Yellowstone area with the introduction of Canadian wolves. Deer, elk and moose populations are plummeting.
The hunter/gatherer lifestyle permits no more than a day-to-day existence, totally dependant on an insecure source of food. Vitamin deficiency diseases are rampant. Sanitation and medication are rudimentary, but cholera isn't deterred by that. Childbirth becomes a trauma that kills huge percents of the population. The eternal nomadic trek allows anything that might be a permanant achievement a waste of time.
So humans alone among animals failed to evolve a competent means of survival until after thousands of years someone finally said, "I know, I know--we can plant seeds then everything will be OK. Phew, that was a close one, fellas--good thing I finally thought of that. Now we can stop all this hunting stuff and instead chop down this here forest and plough all these acres and kill grasshoppers."
That would only have looked like a good idea when population increased to the point that nature was no longer capable of supporting such numbers--only then would people have found farming easier than hunting.
Curiously enough, hunter-gathering was so successful a lifestyle that man increased in numbers until finally he was too numerous to live directly off nature.
But then the scarcity of game would cause the population of predators to fall until there were no longer an abundance of predators, and the game would recover.
Of course if one were to suddenly inroduce a predator species into an area where aninmals have not evolved to meet the threat of that particular species, havoc might ensue.