It's old news now, but this is posted on the search page of the Social Security Death Index at Ancestry.com:
"Why can’t I see the Social Security Number? If the Social Security Number is not visible on the record index it is because Ancestry.com does not provide this number in the Social Security Death Index for any person that has passed away within the past 10 years."
Others have commented, so I won't repeat that here, but I don't think really does one whit to stop identity theft.
