In Sweden your social security number is public information. What's the reason for it being private in the US? Sounds like a horrible thing to rely on for security anyway.
Well I mean, what it comes down to is you need someway of establing that it's actually you over a phone or Internet and you can assume that an equifax-equivalent would be storing that info regardless of exactly what it is in Sweden.
This makes the phone scam a lot more involved because you can impersonate someone on the phone but the mail makes it kind of 2fa. The credit card you tried to open in Bob's name will always be sent to the real address of Bob.
The bank didn't need to store much here - names and addresses they can lookup directly from the id number.