Only a half truth. Borders may have been loosely defined but they were absolutely defended with violence. You couldn't wander in and hunt in your neighbors woods, take their timber or set up a farm too close. Hell, sometimes they even had well defined natural borders or walls (see: Hadrian's wall, the great wall of China)
Moving through an area in large numbers might draw a violent response and you might be coerced to leave if you spoke the wrong language or dressed the wrong way. If you were an unknown group of strangers they may well let your boat sink or leave you to starve outside their walls. Modern states have simply codified these reactions into law.
Proto-states and the associated mechanisms developed extremely quickly once sedentary agriculture became dominant. If your entire livelihood is tied to a field of grain you no longer get to run or hide from conflict; controlling who can and can't get near it becomes imperative.