Actually, CC details never transit to the shop server. The CC inputs don't have a "name" attribute, so the browser doesn't add them in the request. Instead, the stripe javascript catches the submit, sends the CC details to stripe with ajax, and add an hidden input containing an authorization token the server can use.

Of course the customer don't know that, but as a developer I'm very happy not to handle any CC details in my server/app :)

This is why i love paypal.

I don't want to input my credit card info in whatever site, I'd rather do it in paypal.com.

Agreed. That's why it's weird that on eBay nowadays they make it very hard to get paypal.com up in the address field of the browser. If you use the standard workflow it will be in an iframe and you will be none the wiser.