When I was hired as a technician for a small/medium size dealership and going thru all that process, it was so stringent that I thought I applied for a job at NSA nevertheless.
The problem is with rogue construction/roofing/grading companies and people like you and me hiring those cheap hands.
I pass by every day by a designated "laborer site" and it is filled with Mexicans. Somebody must keep them happy!
I think the government is one of the biggest indirect employers of illegal aliens. Check out any highway construction site. Aren't all those contractors being paid with taxpayer money?