No, it's not about any woo woo natural balance. Mammoths were really easy to kill and if they were anything like their elephant cousins would have taken 10-15 years to reach sexual maturity. Their population would also be considerably lower and larger animals are more sensitive to change because they reproduce slower and their are fewer of them.

Buffalo on the other hand reach sexual maturity at 2-3 years, there were many more of them. They replaced their populations faster.

The first humans in North America didn't extinct buffalo because they couldn't, they would have had to have much more population and civilization progress before that became a risk.