I have a paypal account, but only have a credit card linked to it. Its not perfect, but they work. In particular, they're pretty crappy about assigning a standard payment method to each account, but not letting you view and manage those yourself. I threatened to sue them for fraud after they kept pulling money from my checking account instead of the credit card that I very clearly told them to use. That's how I found out.
I then removed my checking account from paypal.