That's why they ask for your SS#. That's what differentiates you from other people. Someone is not helping you correctly. That's the silliest thing I've ever heard. If you shop at Target enough, you should be fighting for that 5% off vs 1% Cashback.
I've been through this many times. I've attempted to sign up with my social, bank statement, check, etc. Once I sign up it request more info in the form of bank statements, proof of address, pictures of my ID, etc. I do all that and it still denies it. I call for clarification and they always say that my name in reference to all others with the same name in my area throws up a flag and denies it.
I'm inclined to believe thats true since it can't be my credit score which is in the 700s. That and I've had similar issues with signing up for other credit cards, phone plans, cable accounts, etc. This isn't just a Target thing for me, it happens somewhat regularly.
I stopped caring about the process as I get the same answer and reasoning each time.
This 1% cashback is great for me otherwise.