If you did not and can not pay for the vehicle, then you should indeed return it. Accordingly, if the credit application was not successful, then that means the dealer did not get paid. Having said that, the notion that you could not use your own bank makes absolutely no sense. Doesn't the dealer take cash? If you use your own bank, then that means you go to your bank, pick up a check, and take that check to the dealer to pay for the car. I'm sure the dealer would be happy to get paid in full that way. So, if I were you, I would go to your bank and get that check if your bank is willing to loan you the money.
As for the claim of fraud, that sounds ridiculous, assuming you were truthful on your application. Accordingly, I wouldn't worry much about criminal charges.
In sum, I would either (1) return the vehicle, or (2) go to your bank, apply for the loan, get the check, and take it to the dealer.
Does that answer your question? Please let me know if you need clarification, as I am happy to continue helping you until you are satisfied.