Here are the last two paragraphs of the Pew report:
Of the several demographic attributes included in the analysis, the immigrant share of the county population is the one that emerges as the most important correlate with the foreclosure rate. And within the immigrant population, the share of foreign-born Latinos stands out as a more notable influence than the share of non-Hispanic immigrants (Appendix Table A5). This may mean exactly what it appears to be—the foreclosure rate among the immigrant population, especially immigrant Latinos, is higher than average.
However, it is also possible that the presence of immigrants serves merely as a stand-in for underlying circumstances not otherwise captured in the data. In recent years, the construction boom attracted immigrants in large numbers into new settlements in the U.S. (Kochhar, Suro and Tafoya, 2005; Frey, Berube, Singer and Wilson, 2009) Many of these areas, such as those surrounding Las Vegas and Atlanta are now witnessing sharp reversals in construction and high rates of foreclosures. The increased presence of immigrants in an area may simply signal the effects of a boom-and-bust cycle that has raised foreclosure rates for all residents there. Thus, it is not possible to affirm that immigration levels in and of themselves raise foreclosure rates.
But, it sure isn't possible from their data to disprove it!
Focusing purely on immigrants (rather than on, say, minorities) is a bit of a red herring. And there is no reason to use some of the Home Mortgage Disclosure Act database on lending by ethnicity without using the meat of it -- the mortgage dollars going to different ethnic groups.
I'm working with a sociologist on a more sophisticated analysis of the data. But, Pew has given us a decent first try.