....Если же летите через другой аэропорт, то пермит вам не ставят, а при получении SSN на карточке пишут, что "valid for work only with dhs authorization". И при всем вашем желании вас на работу без авторизации не возьмут.

...."If you are an alien without permisson to work in the U.S., your Sotial Security card will be marked "NOT VALID FOR EMPLOYMENT". We will notify U.S. immigration officials if you use the number to work.
It you are an alien legally in the U.S. with temporary permission to work, your Sosial Security card will be marked "VALID FOR WORK ONLY WITH DHS AUTHORIZATION". If you show your card to an employer as evidence of employment eligibility, you will also have to show your U.S. immigration document authorizing employment".
Информация взята с приложения к ССН.

.... Некоторые девочки устраивались на работу с SSN и показав что есть НОА

The K-1 symbol indicates you are the fiancé of a U.S. citizen. As such, you are eligible for a Social Security number and for employment. To apply for a Social Security number:

Complete an Application For A Social Security Card (Form SS-5); and
Show us documents proving:
Immigration status;
Work eligibility;
Age; and
Identity.
Take your completed application and documents to your local Social Security office.

A. Introduction
The Department of Homeland Security (DHS) determines whether an alien can work in either employment or self-employment in the U.S. Under certain circumstances, DHS authorizes nonimmigrants to work. Some nonimmigrant aliens have employment authorization by virtue of their alien classification. Some can work but only for specific employers. Others must apply to DHS for employment authorization. Still others are not allowed to work while in the U.S. and cannot apply to DHS for authorization to work.
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B. Policy - Evidence of Employment Authorization
Required evidence for employment authorization is either a Form I-94, Arrival/Departure Record, showing a class of admission that indicates the person can work without specific DHS authorization (RM00203.500C.1.) or an employment authorization document (EAD) (Form I-766 or I-688B).

The following sections list nonimmigrants, by alien class of admission codes, who are authorized to work in the U.S. without specific authorization from DHS. The person’s I-94 will not have the DHS employment authorization stamp and the alien will generally not have an EAD.