One guesses that Ozimek is a wet behind the ears libertarian — let's call him a "wee-wee libertarian"! — in which case the best cure for his condition is to read Derb's Libertarianism in One Country.
Anyway, the appropriate counter to Ozimek's juvenility is something John O'Sullivan wrote in his review of (the late) Samuel Huntington's 2004 book Who Are We?. Saith O'Sullivan:
Huntington punctures several comforting national myths dear to both liberals and conservatives but false and sometimes destructive in their current implications. He points out, for instance, that the U.S. is not "a nation of immigrants." It is a nation that was founded by settlers—who are very different from immigrants in that they establish a new polity rather than arrive in an existing one—and that has been occupied since by the descendants of those settlers and of immigrants who came later but who assimilated into the American nation. Americans therefore are under no moral obligation to accept anyone who wishes to immigrate on the spurious grounds that everyone is essentially an immigrant. Americans own America, so to speak, and may admit or refuse entry to outsiders on whatever grounds they think fit.