Actually you’re not quite correct, you can get a green card through an airline, in fact you can get a green card from any employer willing to assist and sponsor you, the employer however needs to have received an approved Application For Permanent Labor Certification, and then you go through an approximate 18-24 month red tape exercise and if the documentation is acceptable then the right to live and work in the US is issued.....
Don’t wanna get too far off topic here but what you are talking about is not a greencard, it’s a sponsored working visa that allows you to work for a specific company for a specified length of time. This visa can then be extended if you fill certain requirements. After x number of years living and working in the US you can then apply for permanent residency and get a Permanent Resident Card.
The only way to get a green card, without fulfilling the requirements for a Permanent Resident Card, is to enter the Diversity Immigration Visa Program, also known as the Green Card Lottery.
CP