What I meant by Americans aren't naturally born with Russian accents is that Americans born by American families with American heritage and culture don't get Russian accents.
Actually, nevermind. This isn't going anywhere..
You're right, your argument makes no sense at all. Of course characters like Dukov and Moriarity wouldn't have been born into American families with American heritage and culture. But that wouldn't make them any less American. Dukov could have been born into a Russian/American family that still practiced some Russian heritage and culture, and Moriarity into an Irish/American one. Just because someone leaves their homeland and sets up residence in the USA, or even Canada, doesn't mean that they will abandon their original culture and language. In may cases they will even pass on that culture to their children and grand-children. If you happen to have a Chinatown where you live, take a walk there some time and note all the people, even young ones, who are still speaking their original language. There's a number of nationalities that tend to gather together and maintain close ties with each other in order to preserve their heritage and language.
PS: Besides, you're thinking in terms of current American culture, a post-nuclear society would be quite different. There would be small pockets of survivors scattered all over the place, and if some of those survivors had been recent Russian or Irish immigrants, any offspring they may have had would naturally adopt the speech patterns of their parents.