My wife got a call from a guy claiming he was with Social Security, and asked for her date of birth and SS number to verify her identity. She replied "You called me so it's YOU who has to show proof of identity". After some back & forth with the guy, she hung up exasperated. And, as it turns out, the guy was legit.
There are still many organisations who do not understand this basic fact: if you call someone's private number, chances are good that you get the person you're after on the phone. But if someone calls you, that could be anybody... even with caller ID (which can be spoofed). Some organisations turn it around and will call you with: "Am I speaking with mister xxx, last 4 digits of SS number 9999?". Still not to be trusted, info like SS number, date of birth or client number are all too easy to get hold of.