I remember one time I was checking on my parents house for them while they were out of town. Capital One had called and left a message saying that there were fishy charges on his card and they wanted to veryify. They gave an 800 number to call.
I though "screw that!", so I went on the computer to Capital One's website and got their number and called them directly. Turns out the message was legit, but I was kind of ticked at Capital One for doing that. Why didn't they just ask people to call the number on the back of their card instead of giving you the number over the phone to call? Seems like they are setting a bad example to their customers on how to avoid fraud.
Anyway, as to the story in the snopes link, yeah, I would never give out any important information to anyone cold calling me no matter who they say they are or how they try and prove it to me. I always tell them that I will call them back.