One reason Europeans tend to misunderstand America is that they come from comparatively more homogeneous and therefore higher trust societies. America is overall better at integrating immigrants, but a solidarity deficit remains. Result: we don't get the nice socialized benefits. It's not the government as much as the polity.
Europe is anything but homogeneous. There are places in Germany, France, etc that have been under rule by numerous nations. My grandparents considered themselves German and spoke German despite living in Russia.
Regardless I've been screwed over by plenty of folks that look just like me, so what you say comes across as an excuse for the state of affairs rather than owning the issues and seeking to improve it.
The agony of WWII and its collaborators is still within living memory, as is life under the Soviet bloc with its secret police and disappearing people, likewise wars of ethnic cleansing in the Balkans. There are also several large secessionist movements where people actually want to secede, unlike in the US, where that kind of talk is rhetorical[1]. I don't think that kind of blanket statement of 'higher trust societies' can be made; the situation is a lot more nuanced.
For that matter, I think that Americans had a lot more trust in their government before the last couple of decades.
