The reality is that most illegals who have paid in and will never get credit.
Being in the Military is not proof of anything other then being in the Military. It's never been used to prove citizenship. Also, the BP does not do it's own background investigations. The investigations are conducted by OPM, DOJ or DOD, depending on who your going to work for.
The INS used the OPM investigators. I'm not sure who DHS uses, but I would guess that it's OPM.
The problem is the lack of investigators to do the checks, so the checks are not done thoroughly.
Boo-freakin'-hoo