The Israelites under Joshua were undocumented immigrants in the Land of Canaan. The Gibeonites were ordered to become hewers of wood and drawers of water for the Israelites. In modern terms that means welfare, food stamps, free health care, and affirmative action (for non-European immigrants), paid for by the American citizens.
Actually, if this is the kind of hermeneutic you employ, then just about any fanciful thing can be crafted from the text. Using ordinary interpretive principles, the "priest" is wrong (but typically a liberal Catholic.
There is no biblical basis for breaking into a country for financial gain (the excuse used by those crossing the border illegally). There is no analogical justification to say this historical group represents us (or them). And, no the Israelites were not "undocumented immigrants" in Canaan. The land had been given to Abraham 430 years earlier and they were just laying claim to their deed.
Where do the Catholics enter into this? Are they the ones enslaving American citizens (the Gibeonites) and forcing them to provide welfare for the illegal immigrants (the Israelites)? Are you actually arguing that THIS is the Catholic Church's end-state for immigration reform - American enslavement? ROTFL!
Mosaic Law makes reference to Israel being the rightful heirs and title-holders of the land, who are supposed to take physical possession of what they already hold the deed to. Further, once occupied, Mosaic Law applied to anyone and everyone that occupied said land. So once Israel crossed the Jordan River, anyone who occupies space inside the borders (legally or illegally) were now subject to the Mosaic Laws (including any that might govern citizenship and government handouts). And any "undocumented immigrants" who were allowed to stay as "strangers within the gates" were expected to learn and obey those laws themselves....
...when all Israel comes to appear before the LORD your God in the place which He chooses, you shall read this law before all Israel in their hearing.
Gather the people together, men and women and little ones, and the stranger who is within your gates, that they may hear and that they may learn to fear the LORD your God and carefully observe all the words of this law,
and that their children, who have not known it, may hear and learn to fear the LORD your God as long as you live in the land which you cross the Jordan to possess.”
-- Deuteronomy 31:11-13