Unabungler - although there are laws in place with respect to the issuing of green cards the rules often seem to be manipulated.
Some time back a few South American pilots with MD11 endorsements from EVA left and got jobs in the US flying MD-11 freighters.
I believe greencards were issued as these individuals were qualified on type and the US freight carrier needed crews with some urgency.Very convenient and good on those individuals for scoring the coveted green card!
The other points around the green card are the green card lottery (50,000 per year)as well as the hiring of an immigration lawyer in the good 'ol American tradition - sue your way in!
Of course one could always go out and marry a US citizen or if your child is born in the USA you would have rights of residency I believe also.