>if you are relying on a cultural change it isn't a technological fix
If traditional food sources go away and technology provides an alternative food source, that is what people will eat. Culture will follow technology, if that's what people have to do to survive.
EDIT:That mostly applies to the population in the developed world with access to capital, technology and industrial resources that we can use to adapt our food supply. Not everywhere in the world has those resources to fall back on though.
In general, that would be prevented by the fact that the developed world is militarily stronger than the developing world. If some resources are not enough for India or Brazil, they can't take them from the developed world in the style of the earlier resource wars for e.g. oil.
It is not as if the countries lack resources. Their fast growing population does [0]. So far, Europe does not seem to be willing to repudiate the asylum treaties it signed, so the young men always have the option to try and reach Europe(an resources) under the guise of seeking protection. And once they are in, their forced removal is unlikely [1], so they cease to be a resource problem for their country of origin and start to be a resource problem for the new host society.
The military does not even play a role here. All the poorer countries need to do is a) not prevent their own young people from leaving, b) not prevent activity of smuggler gangs, c) complicate deportations by refusing to issue passports to their citizens who destroyed their papers underway. None of those actions need guns, much less superior guns.
[0] ... India and Brazil aren't really in the "top population growth" league. Look up population pyramids of Niger, Ethiopia, Nigeria, Yemen. Those graphs promise future mass migration streams. (https://www.populationpyramid.net)
Military might is not very helpful in the modern world. The NATO coalition could not hold their ground in a country such as Afghanistan nor could all of Europe prevent that the collapse of order in Syria (a country of 20m) caused a spill of 2m migrants into Europe.
Your parent was suggesting that the developed world could not deal with a collapse of India or Brazil or several populous African countries.
If traditional food sources go away and technology provides an alternative food source, that is what people will eat. Culture will follow technology, if that's what people have to do to survive.
EDIT:That mostly applies to the population in the developed world with access to capital, technology and industrial resources that we can use to adapt our food supply. Not everywhere in the world has those resources to fall back on though.