I don't get the reasoning behind that description. Immigrants built the Catholic Church (and the Catholic churhes and cathedrals and schools) in the United States. Immigrants with big families in little houses.
You're right that the immigrants built the churches and schools, and they sacrificed to do it. In THAT regard, their children and grand-children don't resemble them, it's just that they want to identify with their forefathers in the INCOME category. Not true, of course, it's an excuse to not support their parishes so they can spend that money on something for themselves or their children.