Current address can change. The only reason my bank knows my current address is because I've repeatedly informed them, and it took about half a year and some effort from my side to have them update all accounts and records with the correct address. So the FBI has a good chance of scaring some innocent men living in a rental apartment that was used by some bad guy two years ago. In one place I lived, I regularly got payment demands from various credit companies to the name of somebody that (I suspect) lived there 2 years ago at least (I knew who lived there before me, and that wasn't the bad credit person). So address doesn't give much.

You can easily open up a bank account without ever interacting with a person- some banks, like ING Direct, are almost completely online.

It isn't too difficult to set up a bank account in someone else's name without them knowing. It happens with credit cards all the time.