The fact that the OP is confusing a positive claim: "states often exhibit little or no regard for the people outside their boundaries" with a normative claim "states _ought_ to act that way" is plainly evident.
That counties and countries are two different things is also obvious, but you need to offer reasons to believe that they are morally distinguishable with respect to economic growth and immigration.
Your analogy doesn't hold. San Jose is not a country, and it has no legal right to prevent US citizens from entering its borders. If (eg.) more people enter than its hospitals or roads can comfortably handle, then it can appeal to the Federal government for assistance. The US cannot.
I don't think the original statement is entirely true either - I can think of plenty of countries which don't promote the well-being of their citizens - but I would class those as broken countries, rather than trying to say that the notion of a country is broken. Certainly most western countries exist to benefit their citizens.
The analogy holds precisely for the reason that San Jose does not consider itself beleaguered by the influx of immigrants who want to live there. The fact that you could entertain thought experiments in which the net consequences of immigration are negative (e.g., a giant flashmob of 50 million people immigrates simultaneously) does not suffice to show that San Jose's hospitals and roads are overwhelmed in the actual world.
In the actual world, San Jose is not in fact appealing to the federal government for assistance; it is reaping the benefits that attend a growing metropolitan population and tax base. On average, San Joseans are better off when more people become San Joseans, for all the same reasons that New York is a more desirable place to live (as measured by the demand for housing) than Wichita.
I've never claimed that there are no states who do not take their citizens' interests into account. I claimed that states often take little or no consideration of the interests of non-citizens. In absolute terms, for example, malaria is a much more pressing human affair than corn subsidies. But corn subsidies primarily affect people within the US whereas malaria primarily affects people outside the US, so corn subsidies dominate malaria in contest for the attention of the US government.
There are plenty of cases where immigration can be negative, particularly in the short term, so controlling the amount of immigration makes sense.
In the case of corn subsidies you can argue that the political process has been derailed in favour of special interest groups. If you follow the chain from corn -> HFCS -> diabetes and heart disease, it's not even acting in the citizen's best interests.
Similarly, it's also trade issues that make malaria worse than it has to be. Screens for windows would make it much less likely to spread - but the material is too expensive for most of the people who really need it.
I don't mean to distract with the examples of corn subsidies and malaria. I don't think it's terribly difficult to find a plethora of examples in which a state's concern for rather trivial internal affairs dwarfs its concern with globally momentous affairs that happen not to affect its citizens. The fact that the spread of malaria could be, but has not been, mitigated by relatively cheap counter-measures just goes to show.
I am not claiming that immigration is an unalloyed good, nor that there are no caveats to consider. I am claiming that freedom of travel is a human right, and that this freedom is largely compossible with the flourishing of the new states into which immigrants move. I just cannot locate any moral claim I have against people who want to move to the part of the world circumscribed by US borders, nor any moral obligation they would have to recognize one. Where is the argument? I can certainly understand that citizens in certain industries would prefer that immigrants with similar skill-sets not immigrate, but protection from competition is not a human right.
That counties and countries are two different things is also obvious, but you need to offer reasons to believe that they are morally distinguishable with respect to economic growth and immigration.