I suspect EU country vs US comparisons get thrown off as well by EU freedom of movement vs US interstate mobility. We should probably be looking at aggregate EU immigration from non-EU nations when comparing to other developed countries.

Someone born in France but lives in Germany vs someone born in New York but lives in California are both similarly easy from a legal standpoint. However counting the Frenchman in Germany as an immigrant seems kind of dubious given that's kind of the point of the EU.