Tricky
Briefly immortal
From that story it looks like there is an advocacy group who supports illegals. That's not the same as the government putting you "under the microscope". It also looks like there are sometimes errors in matching SSNs, but they are most often typos. I would guess they straighten out the typo and then everything is cool. (Though I am quite aware of how a government bungle can screw up your life.)
I don't know if this is true or not (no source given), but even if it is, it would mean that you can't fire them for using a fake SSN. It doesn't mean that you can't fire them for being illegal, which you discovered when you identified their fake SSN. It also doesn't mean that you can't refuse to hire them without a real SSN.And apparently, it's also illegal to fire someone found using a fake SSN. Nothing like bureaucracy!
But this still ties in with what I said about the government not being serious about restricting illegals in the workplace. These loopholes would be fairly easy to close with simple legislation. That this legislation somehow never seems to make it to the halls of Congress probably has a whole lot to do with the lobbyists for businesses, like the construction industry, making sure such bills don't make it out of committee.
But I'm not saying I would favor such legislation. I don't. I like my cheap labor and cheap prices, but if I had to suffer higer prices for getting the laborers treated fairly, i.e. normal job benefits, I'd bite the bullet. I'm also not into the hypocrisy of blaming the laborers and the landlords and virtually ignoring the people who hire illegals. What do you want to bet that there are a number of people in those communities who hire household workers on a cash-only, no questions asked basis.