From the standpoint of biology, he's right. Those organisms that are most successful are those that have the greatest numbers, and more recently, longevity for those numbers.
On the contrary, there is a reason species fluctuate around a carrying population. Biology builds in a control mechanism so that the delicate ecology in which we find ourselves is not unbalanced. Humans have shattered that ceiling and are in the midst of spending hundreds of years dealing with the consequences. Success is measured by the longevity of a species, not its members, nor the amount of space they occupy. A dangerous misconception that the technoutopianists like to spout (as above). We defy natural laws at our own peril.
I'm not ignorant of biology. But the carrying capacity is determined by the spatial limits placed upon a species. The earth can only carry so many humans (At a specified quality of life) but that knowledge SHOULD drive the process of getting our genetic heritage off-planet, rather than a reduction in total population or quality of life. Carrying capacity is only an issue if we can't establish viable human populations off-planet. We can't yet, but we will.