It's not just that, it's also the fact that to the outside world, the way that the map of the USA is politically depicted is as a set of starkly-contrasting red and blue states, almost all of which stay red or blue, with only a small number changing occasionally. The red states often tend to be mostly contiguous as well. At a glance, to people who aren't really familiar with the USA, that can look a lot like a clear dividing line.
Once people are shown a county-level political map or a cartogram that's deformed based on population, the error with that perspective should usually be obvious, but people aren't normally shown that.
I think it is also worth noting that many EU citizens are going to approach the idea of national change with a perspective that is radically different then the one most people from the USA would have. The tumultuous past century of European history means that European countries are, in general, pretty new. The UK in its current constitutional state goes back to 1922, less then a century. France's current form, the Fifth Republic, was founded in 1958. Germany as it presently exists dates back to 1990. Spain only transitioned to being a democracy in the late 1970s. The Balkan countries in their modern form are about 30 years old. The Baltic countries are even newer.
There's exceptions but they're not common. The result is that many Europeans will not automatically assume that the continued existence of their nation state is assured, because a totally different nation state is within the living memory of their grandparents or parents. In many cases they remember it themselves. The USA, on the other hand, has been relatively steady for over a century - the only change within that time being the addition of Hawaii and Alaska, both of which had long been US sovereign territory anyway. I think a higher percentage of Americans are likely to view the USA as a semi-permanent institution, while a higher percentage of Europeans would be more likely to view nation states, including the USA, as being transient (in many cases from personal experience).