I think you are paranoid. Your SSN is out there already waiting to be stollen. One more business is not going to matter. Heck, for various medical and 401k places from work, either the login or password is one's SSN. Now, one hopes every place that uses the SSN is valid, but one way to protect yourself is to do banking with a place offering and guaranteeing protection from that theft.
But, if they can find your SSN from the last four digits, it's there for the finding. Either don't worry about it or get protection.
But, if they can find your SSN from the last four digits, it's there for the finding. Either don't worry about it or get protection.