I want to see that movie now considering I am not so sure it is a "myth".
Something everyone needs = food
Food supply around the world now is pretty much 100% connected to oil
Oil is a limited resource, reduction in oil production will have an impact on food availability. Food availability will have an impact on the population.
We have electric cars and such, but nowhere near the "electric" or "biofuel" transport devices (trucks, boats, planes) needed to uphold the transport network needed to keep the food deliveries the same as they are now without oil, and not sure if any of those things are in the making at the moment either. So far we seem happy with a few Tesla personal transport cars.
Hence the "over" part in overpopulation, is tied to the resources required.
Same with other resources. If we are to look at what we would ideally like to have, equal rights for everyone in the world, but there isn't enough "stuff". Not everyone in the world can get a car, TV, iphone and a PS4/Xbox. It is a noble goal to say out loud, but an impossibility in practice. If China or India were to become the new growth/consumer nations in the world, then the west would be the ones who would have to go down in product availability to be able to supply them.
I tend to see reason with the writings of Daniel Quinn, as he makes quite a few good points in his books (though few to no answers, but he certainly teaches you to raise questions).
Unrelated to this, but a guy who probably shares Grims mindset.