Did you see the SS card or was the number given verbally? That would influence my decision. If I have an image of the SS card and can verify we didn't transpose a number, I would close out the account and mail the person a check for the balance. If it is possible I transposed the number and couldn't get SS to help, I would require the customer to bring in the card to verify and decide what to do at that time.
A successful man is one who can lay a firm foundation with the bricks others have thrown at him.