This is true - they’ve “watched our movies”...I’ve actually heard that as a reason why “everyone knows the USA”. Smug Canadian’s annoy me the most.
That said, it also annoys me when American’s say to the British, “you owe us, we walked in and won your war for you” (WWII). That’s just as ignorant. Britain was fighting alone for years and far more Brits were killed, if they’d lost the Battle of Britain then the outcome of the war might look very different. We fought that war “hand in hand”.
America is a big place, lots going on...it doesn’t surprise me that many don’t know about much outside of it. That said, those that either go to Europe and fall in love with its architecture and history, along with its liberalism (after a week of vacation), or those that never go there at all and have no knowledge of anywhere...can be equally annoying.
I’ve also met young European’s that have quoted me George Washington (I just about fell over) - so there’s hope yet.
My guess is you’d be lucky to find one in ten Americans who have an opinion about the battle of Britain but 90% of Europeans will have an annoying attitude about America.