> I get the feeling this article is conflating birth rate with actual population growth.

It's not. Fertility rate for the US and the developed world is below replacement. And in the developing world, it has been dropping consistently.

> One reason why people have less children is that more of them survive.

That's a reason why women don't have 5 or 6 children, but that's not a reason why women has less than 2 on average.