The second theory is stupid. Core countries consume way more resources per capita by far than the periphery. It would be a hell of a lot easier to keep people from buying McMansions than it would to keep people from reproducing. The problem is wealth and industrialization. Overpopulation isn't really about people, it is about resources consumed.
How can it be stupid? Look at the graph and it makes perfect sense. The theory has nothing to do with consumption or with McMansions. There are resources available to feed the current population as it sits now. Transport and distribution of the food to the areas that need it is the problem which you know. But as population grows the resources will run out (obviously.) I guess I don't understand your argument as how the theory is false. Believe me, I want to see you prove it wrong. I didn't make it up so it won't hurt my feelings.