For people living in America an identity is a name, date of birth, mother's maiden name and SSN. If you lose these, you could be the victim of fraud.

But you already knew that didn't you? You deliberately misinterpreted what he meant by identity theft.

Mexico and Brazil use SSNs?

I am a USian. The nonsensical concept of "identity theft" has been promulgated by the surveillance industry to avoid responsibility for their own negligence. A person cannot become a "victim of fraud" in the way you describe. The banks are the only parties that stand to be defrauded, and they could avoid this by stopping to pretend that a few bits of semi-public information is enough to identify a person. So far it has been more profitable to keep the gravy train of easy credit rolling, which is fine. But that doesn't mean we should bear the burden for them!

When someone earnest talks about their "identity being stolen", I prefer to think of them as complaining that one of their friends bought the same pair of red Nikes or whatever.