I think that the Social Security Administration database is different than credit records.
I changed everything before I ever developed any credit. I am in a business where I can get all kinds of info on people. I've looked for info on myself using those services, and checked my credit reports too. There is nothing there to cause me any problems. I'm fortunate in that one particular way.
But I went to the Social Security Offfice a couple of years ago and the lady let me see what came up on the screen. There it was. Names, dates, everything. And I changed my info nearly 20 years ago.
I don't know why a bank would have or need a direct feed into the Social Security Administration database, but that is what it sounds like they had.
Most, perhaps all, employers don't get to have that access. They just send in the form you fill out and get a "no match" letter if the reported name or gender or other info does not match the current records. But they are not told in the letter why the "no match" occurred, and the employee has a couple of months to fix it. Recent attempts to force employers to fire employees who failed to correct it within 60 days were struck down in court, last I heard. The Social Security Administration did not send "no match" letters if only the gender did not match until after 9/11. The Bush administration cahged the software. Perhaps the O'bama Administration will change it back?
That does not mean that employers cannot find out information about you, especially if you sign forms empowering them to perform a background check.
We need laws to protect us from this problem. For example, if we have good credit and criminal history, or rehabilitated histories, etc., then we ought to be able to apply for a new social security number, and get a new credit record that is blank, but has a score matching the old credit, and can't be told apart from regular credit reports by anyone checking our credit. I think those laws will come eventually, but probably not in my lifetime.