Just gave it some thought on how it was possible to get an account at Navy Fed without entering a SSN.

I created my account online. And when I call the support line for anything to do with my checkings account they never ask me for my SSN.

But since I have a credit card they do ask me for SSN since it's part of the application process.

So it turns out I don't have my bank account tied to a SSN and haven't signed a signature card perse