You're confusing "Payment Acceptance" with "Payment Processing". The APIs Visa is exposing on that site of theirs are specifically for payments processing - you have cardholder data and you use it for Authorization/Capture/etc. Payment Acceptance on the other hand has many different flavors especially in the 'Card Not Present' environment where the end user checks out on the web site for example. There are multiple strategies for that in terms of PCI compliance - companies like Stripe, Cybersource(which is now part of Visa) etc provide those solutions.