From what I understand you do not need proof of citizenship to obtain a legal SS number....I could be wrong here (I hope I am).
no you don't need to be citizen to get a SS card (a legit one). You just need a "green card".
Many people including those in the congress and senate confuse "legal status" w/ citizenship. Many people here working legally have no desire to be American citizens. They want to keep their home country citizenship.