Here is some accurate info for the "green card ' holders" there is no problem what so ever not getting a job, it just takes 45 days for the paperwork to be completed, I heard this background check takes a lot less time.
This is a direct quote from the Federal register:
"Under section 113 of the Aviation and TRansportation Security
Act, CERTAIN AVIATION PROVIDERS subject to regulation by the FAA
are prohibited from providing training to aliens and other designated individuals in the operation of aircraft with mtow 12500lbs or more, UNLESS the aviation training provider notifies
the Attorney General of the Identity of the alien seeking training
and the Attorney General does not direct the aviation training provider within 45 days that the alien presents a risk to aviation
or national security."