I can't state for certain about up in NY state, but down here the R Catholic Church is a major enabler and supporter of illegal immigration. So much so that if there is a news article that mentions the both the words "immigrant" and "Catholic," you can be sure it has something to do with illegal immigration.
I am not surprised that AZ made that connection, because the RCC in AZ is much like the RCC in Texas.
This is compounded by the thoroughly dishonest way the MSM deals with illegal immigration, as has been discussed here and in the MSM itself.
For my own part, it sounds like there was some significant activity at the location to indicate some sort of legal immigrant classes or folks who were at least trying to go through the system. Also, it seems that the local area was settled with a lot of immigrants from Asia: lots of folks interviewed from one of the 'Stans. This suggests a lot of refugee and asylum types, rather than your run of the mill illegal alien.
That does not preclude the particular charity from enabling illegals at the same location.