I spent several years working at the UN alongside Catholic groups on family issues. I met with Cardinal Martino at the UN Mission. I have hosted the Catholic delegate to UN meetings in my home.
I noticed that they always got very quiet when immigration issues were on the table, and usually took the pro-immigrant position, if they took any position at all. I think I remember being told that the Catholic position was the people should be able to immigrate wherever they want.
Did I misunderstand?
An individual or group of individuals undoubtedly said something along those lines. That doesn't make it 'the' Catholic position. They can't rely on anything in writing to back that position up, because what is in writing requires balance. There are good reasons for people to immigrate but, at the same time, immigrants are required to respect the laws of the host country. That includes laws governing immigration itself.
The American bishops are also doing a bit of a tap dance in relation to the death penalty. They know it can't be declared morally wrong, so they are joining the crowd proposing a moratorium on imposing the penalty.