There's plenty of employers who don't bother with checking their employees' status. If you're a contractor, for example, you hire a bunch of illegals and pay them in cash. You then list them as "sub-contractors," rather than as "employees" when doing your paperwork. You don't have to check the immigration status of a sub-contractor.
Other companies just don't bother checking their employees' immigration background. They don't need to- there is a very small chance that they will get caught by the INS. Big corporations exert pressure on Senators and Congressmen (of both parties), who exert pressure on the INS to not do many raids on those corporations.
I would think this would have been all over '60 Minutes' or the 'O'Really Factor' years ago. It would be painfully easy to expose. Hire a guy to pose as a recent immigrant.\, have him wear a wire and record every step of the hiring process in 5 or 6 different suspected companies.