There are debit and prepaid cards, that can be used online, but disputing fraudulent charges is next to impossible. There are non-US banks, where disputing fraud is extremely difficult and takes months, during which your funds remain blocked. There are many cases where a card wouldn't work because it is from a different country, but PayPal works.

International consumer finance is a mess. Not everybody who shops on the Internet is a US citizen with a credit card account in a first-rate bank. There are other options.