Without denying that those of us in wealthy societies may have extremely demanding duties of global distributive justice, I ultimately reach the stark conclusion that every legitimate state has the right to close its doors to all potential immigrants, even refugees desperately seeking asylum from incompetent or corrupt political regimes that are either unable or unwilling to protect their citizens’ basic moral rights.
But, reading on, it's not so clear that this really is what he concludes. In a key passage on p.127, he writes:
[I]f wealthy couples need not open up their marriages to those less well off, why think that wealthy countries must open their borders to less fortunate immigrants? Just as relatively wealthy families are required merely to transfer some of their wealth to others, why cannot wealthy countries fully discharge their global distributive duties without including the recipients in their political union, simply by transferring the required level of funds abroad?
Certainly we could do this. So immigration restrictions might not be unjust were we to fully discharge our obligations to the global poor by other means -- just as blocking starving Marvin's access to the market would be okay so long as you instead provided him with all the goods on his shopping list. But given that we aren't otherwise meeting people's basic needs, preventing them from doing so remains pretty clearly wrong.
Wellman's commitment to something approaching open borders becomes much more explicit on p.137 (emphasis added):
[So long as concerns about illegal overstaying can be addressed], then the arguments for limiting immigration offered in this article would leave much more room for freedom of movement than the status quo, since it would allow most people to travel freely around the world (as tourists, to family or doctors, or even to study or work) as long as they did not stay indefinitely in some place without the permission of the host political community.
Effectively open borders without citizenship (albeit with whatever time-limits, if any, one believes are needed to avoid an obligation to grant citizenship) seems a far cry from a state "clos[ing] its doors to all potential immigrants"!