Knowing that TV and social media do play as large a role as history books or formal education in knowledge acquisition these days, is it really wrong to question whether "the average person" is a valid point of reference when discussing inter-civilisational exchanges of discoveries.
These days, I've come to treat every clean-cut historical anecdote as suspect; there's too much of a game of telephone between people who want history to prove their point.
The Renaissance really was taught as "Europeans rediscovered the great classical thinkers", and it was only through my own curiosity that I learned that Islamic science played a key role.
("Gravity... ha yes, the guy with the apple","evolution... sure, we all are descended from apes, right?")
...Therefore, relying on what the average person may know to discuss whether something is publicly acknowledged and understood is perhaps the wrong way to go about this.
This massive gap in the common understanding of the way the modern world came to be is concerning; undermines most people's model of the development of civilization is, for example, one of the things that makes it easy to drop bombs on historical sites (and the descendants of those who built them), or to ignore when other parties do the same. "Ignore what the peasants think, only elite thought matters," has never preceded an era of sustainable peace and prosperity.