"I'm glad to let you know that you qualify for X healthcare coverage. Can I just have your social security number and we'll send over the confirmation documents?"

Yes, people fall for this kind of stuff all the time.

In many cases it's much easier than you'd expect. See e.g. http://www.heinz.cmu.edu/~acquisti/ssnstudy/ (TL;DR: "we show that it is possible to predict individual SSNs simply from publicly available data").

ehrm in sweden, yes.. those people are so mad that they allow a reverse search!!! I made payment gateways for companies there and was surprised by that.

What's really sad is that, if all those phone numbers were already public, I guess nobody would have cared to create something like SnapChat in the first place..