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.
Oh, I agree. Western civilization and specifically the idea of human rights, is a hybrid of classical and Hebraic civilization. This is more than a little weird, as the two aren’t really compatible. The Romans could get along with just about anybody, but not with the Jews.
One theory about the unusually long vitality of western civ, going on 1000 years now, is that this hybrid nature provides a type of “hybrid vitality.” The internal struggle within the society keeping things from stagnating as tends to happen with a less diverse society.
We may be seeing the end of western civ approaching, but then people have been saying that for 500 years or more. Which doesn’t mean it can’t be right this time.