You have to show credit card or SSN. No SSN means no credit card. No one will take Debit card for rental propose. You have to show Credit card and you can pay from Debit card or any other methods though.

Anybody can rent car and add your name on it, it doesnt necessarily mean he has to pay. You can pay while returning the vehicle. For accidents and everything you will be responsible but when the car is lost (worst case), they will catch the credit card guy.

SO you have to make him/her believe that you are not fleeing. It should be easy for you

Good luck !