Not true. I have a SSN and have never been a citizen or a resident. I got it many years ago (like in 1992) when I wanted to open a US bank account and they said I needed a SSN. This was pre-ITIN, which they now issue to non-residents for tax purposes. Mine says 'not valid for employment' on it but it functions exactly like a regular SSN in every other way. The only drawback is they will not, under any circumstances issue me a new card. I changed my name when I got married in 1995 and a few years ago, I went to a SS office to get a new card. They will not do it. They changed their records to reflect my new name but will not issue me a new card until I can show them a visa or green card proving lawful presence in the US (I live in Canada). I even tried in Hawaii where I now own a home, bringing all sorts of bills and property tax statement but nope. Without a visa, no new card. So I do have a nice, valid SSN which I am very lucky to have gotten.

Also, don't all lawfully present (i.e. Visa holders, green card holders etc) get issued SSN's? They need one to work and they are not citizens.