Ummm... Not exactly.
First of all, "Europeans" tend to know a great deal more about the US than Americans know about Europe... a ridiculous amount more, actually. The fact that Americans tend to lump them all together as "Europeans" suggests that they know very little about the various countries and cultures that make up the EU. There is sooooo little in common between a German and a Frenchman that it makes comparing a Californian and a Texan seem like a joke.... and Germany & France actually share a border. Along the Rhine and in the Alsace in places like Strassbourg there is considerable crossover, but to lump Portugese from Algarve in the same category as Finnish Laplanders is laughable at best.
Secondly, America is still a very racist country... and so are many European countries. Openly racist politicians from the far right have been making huge gains all across the region for quite some time now. From Holland's Pim Fortuyn List to Switzerland's SVP leader Blocher... from Austria to France, Italy to Denmark racism, xenophobia, and nationalism have been on the rise in Europe for over a decade. These countries had fairly liberal immigration policies that began to dilute their precious national identities, and the backlash has been in full effect since the mid 90's. Furthermore, the colonial countries still have lingering prejudices from their empire days. It is only natural that they identify with America's historical problems with multiculturalism and race.
Third, Europeans tend to encounter a very specific segment of the American demographic... namely that of the moderately well-heeled, slightly provincial, "ugly American" tourist. Of course they sometimes see the more sophisticated "jet-setters," and they see loads of bright-eyed young "backpackers," but all three of these groups represent a very sheltered, lilly-white version of the US. Aside from the constant flux of entertainers, musicians, DJs, and artists, most Europeans don't really get to see any authentic urban type Americans... let alone any truly poor country folk, trailer-trash, or ghetto hood-rats. Their understanding of our social dynamic comes primarily from our TV, Film, and Music... and our foreign policy. So, whatever their view of us is... we gave it to them.
I think it is fairly arrogant for Americans to berate Europeans for assuming that we are a racist country based on our own recent history, the face we show to the world, and our portrayal of ourselves in our media... when less than 10% of Americans have even the slightest clue where Andorra is or what language is spoken in Luxembourg. Hell, most Americans don't even know that we call places by names that they don't use themselves... like: that there isn't actually a country called Germany! (They call it Deutchland... no Bavaria, that's Bayern... no Spain either, that is EspaƱa etc. etc.) And then we get haughty that they don't know current migration trends among African-Americans?
Please. After all, it's only been just over 40 years since lynching blacks was a fairly common occurrence in the good ol' US of A...