I think the assumption was that humans would continue growing exponentially until they reach the carrying capacity where they're all fighting for the same resources. Then the population stops increasing because there's not enough food/water/shelter to go around.

What actually happened is people in rich countries have plenty of food/water/shelter to continue reproducing... if they wanted to. The thing the models didn't account for is that people would choose to have fewer children based on standard of living.

To me it seems this had nothing to do with the standard limits of nature, but based on individuals' choices. Given those models' assumptions, I think they were valid. I would have made the same assumption based on past data as well.