2241 The more prosperous nations are obliged, to the extent they are able, to welcome the foreigner in search of the security and the means of livelihood which he cannot find in his country of origin. Public authorities should see to it that the natural right is respected that places a guest under the protection of those who receive him.
Political authorities, for the sake of the common good for which they are responsible, may make the exercise of the right to immigrate subject to various juridical conditions, especially with regard to the immigrants' duties toward their country of adoption. Immigrants are obliged to respect with gratitude the material and spiritual heritage of the country that receives them, to obey its laws and to assist in carrying civic burdens.
It seems Roger Cardinal Mahoney loves paragraph one, but has taken Witeout™ to paragraph two.
I also found via a search on the Vatican website a statement issued by John Paul II for migration day of 1996. He is very clear, nations have the right to secure their borders and to stop illegal immigration into their countries.
He goes so far as saying when an illegal can not become a citizen because of laws or other considerations it is the Churchs job to "ask them to leave". Completely different from what Mahoney is doing/saying.
http://www.vatican.va/holy_father/john_paul_ii/messages/migration/documents/hf_jp-ii_mes_25071995_undocumented_migrants_en.html
Highlights
"Illegal immigration should be prevented, but it is also essential to combat vigorously the criminal activities which exploit illegal immigrants. The most appropriate choice, which will yield consistent and long-lasting results is that of international co-operation which aims to foster political stability and to eliminate underdevelopment"
"4. When no solution is foreseen, these same institutions should direct those they are helping, perhaps also providing them with material assistance, either to seek acceptance in other countries, or to return to their own country"