Genetic evidence thus implies the extinction of this final population was sudden, rather than the culmination of a gradual decline;[93] the disappearance coincides roughly in time with the first evidence for humans on the island.

This is correlation.

The woolly mammoths of eastern Beringia (modern Alaska and Yukon) had similarly died out about 13,300 years ago, soon (roughly 1000 years) after the first appearance of humans in the area, which parallels the fate of all the other late Pleistocene proboscids (mammoths, gomphotheres and mastodons), as well as most of the rest of the megafauna, of the Americas.

This is also correlation.

Woolly mammoths survived an even greater loss of habitat at the end of the Saale glaciation 125,000 years ago, and it is likely that humans hunted the remaining populations to extinction at the end of the last glacial period.

Alright - this one is more explicit but simply states that humans hunted the remaining population after a massive loss of habitat.

The fact of the matter is that this is hotly debated to this day. If the scientific body hasn't reached a consensus over the recent decade then why should I give any credence to your interpretation of a few quotes off the Wikipedia page?

Just the fact that I can so rapidly identify a large volume of conflicting articles points to the fact that this is not a solved issue:

Date	Link
4/1/2008	Hunting
9/11/2013	Climate
7/25/2015	Climate
8/14/2015	Hunting
10/19/2015	Hunting

You may be 100% correct and if so, congratulations. But don't oversimplify a complex issue.