I never got the impression that the EU was been marketed as 'one country'. The original concept was created after WWII to try and create an environment to discourage war in Europe, making it one big happy family with a common market for our produce.

I lived in London for fifteen years and their contempt for all things EU (based on it not being British and a long held mistrust of Johnny Foreigner) was to say the least irritating. Meanwhile their politicians seized upon the business opportunity it was and ran with it, blaming any unpalatable decisions as being EU based further disenfranchising the general populace. Or maybe that was just their media doing the blaming.

I think the EU tries to make all member countries apply best practice in the managing of the country without affecting the indigenous ethnicity. That said, being bureaucrats the actual civil servants would have no qualms about impacting the indigenous culture if they got away with it but for every decision we do have some redress even if that is through the European courts.