I use Paypal for one reason (as the consumer); it adds an extra layer of protection for me. I don't want to give my CC details to every site I buy from. And then have to check my CC statement everyday to make sure nothing was hacked along the way.
For a consumer, Paypal makes it very easy to manage payments, receipts, and any other issues.
By the way, never ever use a debt card online. You're handing over access to your bank account.
My personal bank also has similar verbiage for my debit card. They also mention that internet purchases are considered non-PIN purchases and are offered the same protection.
Yes, there is more risk since money can be taken directly out of your account instead of going against your credit, but there are mitigations in place.
I repeat this almost every time this topic comes up:
With a credit card, you can say that the charge was fraudulent and they will take the charge(s) off and you're not on the hook. With a debit card, you're out the money of the fraudulent charge while the bank investigates. From my personal experience, this can take a few days to 3 weeks before the bank puts the money back in your account. If the charge happens to put your account into overdraft, you may still have to pay the overdraft fee which may be hard to get overturned.
I pretty much only use my debit card as an ATM card. Very rarely do I actually use it as a debit card (there are rare instances where I may need to)
Conclusion: Don't use your debit card online if you have a credit card.
Used to work in the industry manufacturing and programming these cards. You are exactly correct, the credit network provides more protection for the cardholder than using your debit card.
With the bank account, they may not reverse fees or other issues that arise as a result. For example, I had a fraudulent charge on a debit card. They reversed it, which is fine, but i was still hit with an overdraft because of a scheduled ACH payment which, at that time, dragged me into negative balance. So there are differences between debit and credit cards.
For a consumer, Paypal makes it very easy to manage payments, receipts, and any other issues.
By the way, never ever use a debt card online. You're handing over access to your bank account.