You're talking about those reloadable debit cards, right? The ones sold on the kiosk along with the gift cards? The Visa Vanilla card does not require a SS# in order to activate it to use on the internet. The activation process only asks for a zip.
However, if one wants to reload that same card or make recurring payments with that card, they want a SS#. Perhaps one can put all 9's or 0's if one doesn't have a SS#?