Europeans, and even Brits, don't get Americans right because they fail to understand the basic nature of Americans. Our natures are made up of a composite of the natures of the peoples of the world and not just one tiny slice of it like the Euros. There is no "typical American" like the types you might find in many countries. But there may be a more rebellious and potentially violent streak in Americans than in other peoples.
But that stands to reason that our country would be composed of these types given the fact that most of us voluntarily chose to leave our places of origin. I do not apologize for our peculiar (in the best sense) nature. If it wasn't for us semi-violent, dimwitted cowboys, the rest of the world would either be singing the Horst Wessel Lied or The Internationale.
We are more violent than Europeans ever were, but never in their vicious, jackbooted way. We are more religous than Europeans are but never in a state church, holy war way.
Our violence and our piety are not laced with statism as the European varieties. Now Europeans have purged violence and piety from their cultures but kept the statism.