"Human society would not function if that was the case."
What do you think's happening RIGHT NOW? With social structure strained, things are getting rather dicey.
"Humans function best in small groups. Introduce any pressure on environmental resources and there will be competition between groups."
Those "other tribes" become the "neighbours" I mentioned, so my argument still holds. When the basics aren't so hard to get (read: you don't have to hunt everyday just to have dinner), the necessary size of the "tribe" shrinks until it's down to family units (houses, neighbours, etc.). Especially when a larger social structure creates a disconnect between the top and the bottom. Instead of food and water, it's spouses, good schooling, connections, and so on. It's the same thing as the jungle, only structured a little differently.