The service provides an alternative payment option for users that may not have access to or wish to use another form of payment.

You can also use a debit card/bank account, I think.

Paypal's not itself a bank in the sense you seem to be thinking of, it's a middleman service for banks and various corporate accounts. Like a normal line of credit, the company managing the service still has to have an actual bank backing it up that both parties recognize.

The service can handle one-time wire transfer type stuff too, in theory, but CCP's end doesn't support it yet. The page you're linking seems to be saying they'll get to it SOON(TM).

PayPal
What is PayPal and how do I use it to pay for my EVE subscription?

PayPal is a payment service through which users can pay for their EVE accounts. The service provides an alternative payment option for users that may not have access to or wish to use another form of payment.

You will need to have a PayPal account to use this method, if you do not please create an account via their website.

During the registration process you can choose between linking your credit card, debit card or banking account (availability depending on your location) to your PayPal account, which will then be used to pay for your EVE subscription.

You can choose to make the payments recurring by checking the appropriate check box and should you wish to cancel the recurring payments follow the cancellation directions posted here.

Please note: eChecks cannot be used through PayPal at the moment. We are working on making it available.

I would have thought that this sentence regarding PayPal from the page you have linked would explain the situation perfectly:

And once again you post a link which clearly shows that you don't need a credit card.

I give up.