All POE's issue that stamp, it is only stamped in the passports of people entering the USA on an IMMIGRANT VISA such as CR-1 and IR-1.
I-551 makes passport into an temporary GREEN-CARD good for 1 year.
If you want the I-551 stamp, you need to marry first, and then apply for a CR-1 visa and enter the USA using the CR-1 visa, Immigrant visas are the only ones guaranteed to be able to take a job immediately after entry to the USA.
You may be thinking about the EAD stamp, it is not USCIS policy to issue this stamp, it is optional, and JFK POE does it as well as others, I have read many posts where people have got the stamp at other ports of entry. JFK can also discontinue this at any time, the stamp is not required to get a SSN from SSA.
K-1 is "Work Auth" primarily to be able to get the SSN, some states are strict in their interpretation of a federal law that requires persons applying for a "license" to have SSN, this can cause a problem with marriage license if only one person has SSN and the other (the K-1 holder) does not.
K-1 is NOT a work visa, it is a marriage visa.
QUOTE
5.5)...Is there any way I can make absolutely, positively sure that my fiance(e) will receive work authorization so that they can go to work and help to pay the bills right away?
A..No.
http://www.visajourney.com/faq/k1k2visa-enter.html#5.5