Yes, there is no contradiction.South america is not advaned. Utilizing technology developed by others is not what I refer to as advanced, which is probably where our misunderstanding comes from. Advanced is referring to an economy built on engineering and innovation. The creators of said technology are advanced.
Did you realize that over 95% percent all work 100+ years ago was physical in nature and oftentimes monotonous? Mostly in agricultural. The ability to perform low-skill, physical tasks is what made a nation and that was brute strength (use of body) more than use of mind.
We are talking about economics and not military, so not even sure why you are talking about armies, but even in the case of armies it is true. The bulk of the roman empire, including the soldiers themselves, but even the much larger bulk which was the farmers that fed those soldiers were based on low-intelligence, high-physical work. That was the base of power of the roman economy. Even today keeping it to the military, since that is what you brought up, we are evolving from mere meat shields into soldiers that need to perform complex tasks operating drones at the soldier level (not just generals), etc.
Of course intelligence is always important, but the ratio of it's importance changed. Today, less than 5% of the US is employed in agriculture (primarily low skilled, monotonous work). Instead, they are being employed in things that require less use of body and more of the mind. Tasks that require abstract thinking, planning, etc that is more associated with higher IQs.
Europe was a backwater settlement in comparison to asia throughout most of history. Here is a chart of historical GDP between the regions:
http://www.marketoracle.co.uk/images/2012/Jul/china-economy-3.png
Europe wanted a more efficient route to Asia because Asia is where the world was centered at the time. Just like today everyone wants a route into the US. It was the same back then that everyone wanted the best route to Asia.