[wideawake]

There could be no residency papers to fast track if they were merely illegals. Enlisting is not a basis for residency. If papers were there to fast track they already had a basis for and a pending application for residency BEFORE they went to sign up.

Here's how it works:

ILLEGAL: I want to sign up, ese.
RECRUITER: Great! Are you a US citizen or legal resident?
I: Um, no.
R: Well, you can't fill out an enlistment request unless you are a citizen, a legal resident or a current petitioner for legal status.
I: Oh? What can I do?
R: I would advise you to find an immigration lawyer and have him file a residency petition on your behalf. If you have such a petition pending, you can fill out an enlistment form and we can get started.

A few hours later:

I: OK, ese, I paid the immigration lawyer around the corner $150 bucks and his runner filed the paperwork at the courthouse and I brought you back a notarized copy.
R: Great! Let's get started!

[drpix]

  R: I would advise you to find an immigration lawyer and     
       have him file a residency petition on your behalf.  If you 
       have such a petition pending, you can fill out an 
       enlistment form and we can get started.

On what basis would the lawyer file a residency petition? Illegals are illegals because they have no basis to file for residency. (Not because they didn't think to see a lawyer.)