I had a debit card that could be used online when I was 13, with my own account, and that was 15 years ago. I know debit cards are not as popular in the US, but I'm fairly certain 13 year olds can have them nowadays.
Debit cards are extremely popular in the US; every checking account by default comes with one, which can be used in any ATM or till that can process transactions on either a credit or a debit network. It is by far the most common means of paying for purchases, and has been so since the advent of the capability. (And, yes, we're getting chip-and-PIN now, too.)
I didn't get my first checking account (and bank card, which only worked in ATMs) until I attained legal majority and started my first adult job, but that was quite a few years ago now. I would be entirely unsurprised to learn that many, many teenagers today have bank accounts and debit cards of their own, even if it's only their allowance that gets deposited there.
>Most teens do not have a credit card or access to their parents' on Amazon.
You would be surprised how many 5 year children make one-click purchases on their parents account. Suddenly all their favorite toys begin to appear magically at the door.