Perhaps they first articulated it. Sure didn't do a very good job of hanging onto it, though!
BTW, their individual liberty was always premised on the existence of a large slave class allowing them the leisure to exercise their personal liberty and think fine thoughts.
The liberty of the America Revolution is actually based more directly on Christian theology, which states that all men are children of God and therefore in some ultimate sense equal. This is a much more solid foundation for liberty than the rather selfish desires of classical aristocrats. This idea of human equality never crossed the classical mind, or indeed that of any other human society.
I think it was based on both. They started with your premise, then asked themselves, "How are we going to get there". It's the "How are we going to get there?" part that they turned to the writings and musings of Greek philosophers and especially on Roman politicians, like Cicero. They relied on Christian principles to define their goals and principles, and classical thinkers to help design the mechanism that would satisfy those goals and principles.
While one hates to generalize, I think it's fair to say that Asia, and most of the cultures contained therein, gave much more weight to military strategists that spoke to conquering enemies, controlling populations and building wealth through acquisition rather than through multiplication.