Rather than edit the previous post, let's expand here. In the segment about the Clovis people, geologist Kennet says that the Clovis people could not have caused the extinction of mega-fauna because North America was too big, and the Clovis people did not have helicopters, machine, guns, and GPS technology. He might be a crackerjack geologist but as a large animal biologist, he is certainly out of his league. A predator does not have to be the proximate cause of death for every single individual of a herd in order to wipe them out - it is sufficient only to reduce their numbers or skew their age-distributions such that the herd cannot survive.
Remember that very large mammals (even today, which are much smaller than their pre-extinction relatives) have long gestation periods and long dependency-periods for infants. If someone moved into Africa and said "Mmm, baby elephants are not very fast runners, and not very wary of traps, and they taste good, and they are about right for the size of our tribe as we kill for meat and follow the tuskers" how long would the African elephants last? A small group of human hunters could have a pretty significant effect on the viability of elephant herds that way. Not so much gnus, wildebeest, antelopes, etc - they could have the most significant impact on the very largest herd animals with the fewest natural predators. Herd animals that relied heavily on herd-behavior to protect the weakest from predation...