I looks like it is basically online banking. Many banks offer this service; this one just has a fancy online face. PayPal has FDIC insurance. Surprise!! It is just a bank also.
I guess you will need to find a bank that still offers Passbook accounts, if you don't want electronic control of your account.
I've read conplaints about PayPal fraud protection not being very good. I agree with that, however what bank checking account with a credit feature has any at all; which is really all PayPal is once you strip away the HTML.