No, my assumptions were almost as narrow as the parent's worldview.
Saying something doesn't make it so. And you can't just say what you wish were true. You have to review the facts and see if what you're saying is actually true or not... For example:
and the typical American who makes broad assumptions about the rest of the world without actually ENGAGING with it
You're making a pretty broad statement there. Assuming anything to be true about the "typical American" is, almost by definition, a broad assumption.
So, no, your assumptions were not narrow by any stretch of the imagination no matter how much you'd like to believe they were.
Oh, I do so enjoy engaging with the rest of the world.