That's part of it, sure, but that's not the whole story.
I've never been to Britain, or to continental Europe, but everything I read (and I have a strong interest in immigration and assimilation) suggests that there is a fairly profound cultural difference between the U.S. and the folk "over there". Despite the nativist and anti-immigrant attitudes that occasionally bubble to the surface here, Americans are egalitarians to a much greater extent than our European cousins. Immigrants here who make an effort to "fit in," and genuinely feels themselves to be participants in the American experience, and embrace (however much in their own ways) American ideals and values, generally are accepted by the vast majority of Americans AS Americans. One can come here from elsewhere and genuinely become an American. I don't mean in terms of aquiring legal citizenship (although that is more doable here than in most European countries) but rather that one is accepted at a social level, and in terms of myriad daily interactions, as part of the national and local community.
The impression I get is that this doesn't tend to happen overseas, especially in continental Europe. Even the most earnest assimilationist immigrant is, in many respects, fated to a lifelong "outsider" status. Sure, there are radical Muslims over here in America, but I suspect far fewer by percentage than almost anywhere else. There are paths to social particaption here that provide alternatives that aren't as available to Muslim immigrants, or second generation immigrants, overseas. The availability of genuine opportunities for integration and acceptance render radical attitudes and approaches less "socially acceptable".
Sure we have significant problems with assimilation here in the U.S. For the matter of that we are doing a very poor job "assimilating" native American children in the values, principles and history of America, leave alone the immigrants. Nevertheless we still do it better than almost any place else in the world.