For most websites that use the Stripe widget, the website owner can never see the full card number, because the credit card number entry fields are iframed in on the page. That means website owners in this scenario are PCI compliant just by filling out PCI SAQ A (self assessment questionnaire A), which is for "Card-not-present Merchants, All Cardholder Data Functions Fully Outsourced": https://listings.pcisecuritystandards.org/documents/SAQ_A_v3...
But that questionnaire is only for merchants where "Your company does not electronically store, process, or transmit any cardholder data on your systems or premises, but relies entirely on a third party(s) to handle all these functions;" For e-commerce merchants who CAN see the card number, they need to use SAQ D, https://listings.pcisecuritystandards.org/documents/SAQ_D_v3.... This includes additional requirements and I believe stuff like a pen test to be PCI compliant.