I'm sorry, but this is just as bad as the idea of European exceptionalism. By any sane metric the Europeans of the medieval/renaissance era had a far better grasp of the multitude of people on Earth then any American inhabitants. The Europeans at the time knew of people on three continents comprising almost two thirds of the total landmass of Earth. The expressed reason for sailing due West from Spain was to find a quicker way to China, to facilitate trade with the Far East without having to go through the lengthy, prolonged and expensive route of the Silk Road (and to bypass those pesky Ottoman tolls in the Levant). The Europeans might not have anticipated the massive landmass that was the Americas between them and Asia, but it was a far lesser revelation to them than the appearance of Europeans was to Americans. One should also be careful to homogenize "Americans" too much, because there was a vast difference between the different Americans of North America, Central America and South America and all of them had even further subdivisions. It is uncertain if the Inkas, for example, knew of the North American Great Plains Tribes and vice versa, but you can rest assured that the Portuguese most certainly knew of the Ottomans and even the Indians and the Chinese. Without making a judgement call on it, Europeans on average probably knew more about foreign people then Americans did for pretty much most of recorded history. Considering the difference in geographical location that's to be expected and is not a statement about superiority one way or the other.
Also, let me just point out that it is impossible to have an oral history that extends 13,000 years back. Heck, reliable oral history rarely extends more then a generation or two back, if that. A story told enough times will eventually morph and become distorted. The Norse had a strong oral tradition, but whatever historical truths one might find in the Eddas is so obscured by generations of oral tradition embellishing, changing and omitting that it is impossible to tell what it is. Most of Europe had a strong, shared oral tradition for several centuries, but today those shared stories are very, very different depending on which country you visit. I really, really doubt that North Americans are somehow superior in possessing perfect oral recollection or that your oral recollection is not as strongly influenced by mythology, superstition and agenda setting as everyone else's. If anything, lacking recorded history is a great drawback because it means that apart from whatever the agenda setters deemed important (and thus shared as oral history) everything else is lost to time. You can never do the Babylonian thing and find old warehouse records that not only talks of the things in store but the names of the people managing the warehouse or the Dead Sea scrolls thing were you suddenly discover tons of forgotten religious scripture. A culture with only oral history is lesser for it because what's forgotten is forever gone, it can never be rediscovered and shared with later generations.