"... since back in the Middle Age's it was widely accepted the Earth was flat too."
Bzzt! This is a widely accepted myth, thinks to a single supposition in a 17th century "enlightment" text that got widely quoted as fact rather than supposition. In fact, the myth is propagated in exactly the fashion the topic started mentioned, where certain textbooks just repeat each other. The earth being round was mathemathically shown in Alexandrian Egypt, if not prior. We have surviving texts. We have nautical records that show this knowledge was never lost--as if looking at the horizon wouldn't clue a couple of bright guys anyway.
Now just why did this myth get started? It was because some people had a vested interest in making the "dark ages" look less informed than they were. Like everything else human, this tendency cuts both ways. No doubt many cultures outside Western Civilization have had contributions that got discounted. No doubt some trumpting their vast contributions today are motivated more by agenda than reality.
Any theory that depends on the idea that a wide swath of people somewhere or "some when" were noticably stupid or gullible or brilliant or "nature loving" is probably motivated, at least in part, by tendencies that will find you selectively picking through the evidence.
The western enlightenment could have kicked off after 1300, but the plague arguably set it back two or three centuries. It's hard to say how "smart" people would have been in, say, 800 France, if they weren't scraping to rebuild a political order. Who knows what the Iroqois (and related tribes, like the Cherokee) would have done if exposed to the alphabet 1000 years earlier. They picked it up darn fast, once they got the idea. What if Japan had been more like England (in several different ways)?
Of course, Civ has always dodged this question because they want the "stone age tribe" you start with to have certain characteristics for game play. Otherwise, you could pick any little tribe you wanted (or even made up), and then develop it how you chose. For the game to ever satisfy everyone (outside of the very nice modding options), it will be necessary to have a lot more flexibly options of emigration and immigration, mixture of cultures, and even surviving through apparent wipeouts. But who wants to play a situation where you don't get to do anything for 100 turns while your scattered people recover from disaster?