It may not be a matter to you since there is no attorney-client relationship yet. But an attorney also has a duty to former clients. The attorney would have to check whether any client he represented before had any conflict with you and whether he had material information in that relationship, which could prevent him from even talking to you, let along representing you in the future. The information he obtains from you could prevent him from representing other clients in the future, not due to conflict of interest but due to confidentiality reasons.
One example. In a small town there were two famous divorce attorneys. A woman divorcing her hu*****and was smart enough to interview both of them, although only hired one of the them. Now since the other attorney obtained material information in the case, he is prohibited to represent the hu*****and in the case. The hu*****and would have to go out of town to get an attorney for himself.
It is a precedural issue and your SSN will be protected by the attorney.
