The ability for a person to live in the place of their choosing is a human right. We have the human right to survive. And if we cannot survive in the place we are, it is our human right to be able to leave. Not all people are born into countries that are able to handle them, and in turn, other countries need to accept the burden of taking that person. The well-being of thousands of people should automatically outweigh a government's right to control its borders.
How a country controls its borders, to a certain extent, falls in line with how they deal with refugees. Most countries have screening processes (with the U.S. process being the most extensive, taking some six months to get a "yes" or "no" on the subject of whether to let refugees in or not) which determine if someone is eligible to be considered a refugee. The problem with most countries, today, though is that, their screening processes are either not extensive, or not specific enough, that is to say weak. There are a number of countries which allow for the automatic admission of refugees, without determining whether these people are actual eligible or not. There are even studies which show that there are numbers of refugees which are not actually refugees at all, but people taking advantage of a certain situation, which posses a particular threat to a country; while the number might be low, it still presents a particular kind of threat, in that, if you can simply take advantage of a system, you could slip into a country and benefit from it, effectively taking the place of someone who actually deserves to be in your position. If a country chooses to close it's borders to immigrants, that does not necessarily mean the country is averse to allowing in /refugees/, as they are two different types of people. It may also be a matter of the situation. In war times, one might be more inclined to say that there is a great obligation to allow the entrance of a greater number of refugees, though lesser instances (natural disasters, depending on their severity!) may not qualify such open policies as times where individual lives are actively at stake from the threat of either prosecution or military threat.