When Amazon user subscribes to Amazon Prime (separate from Prime Video), it is bound to same region as the one used to login to main Amazon website. For international users this is most likely Amazon USA, Amazon UK or Amazon DE depending on where they initially shopped.
When Amazon Prime detects that region from credit card does not match the region of the website, it suggests transferring the Prime subscription to another Amazon website, for European users, this would most likely be Amazon UK.
The catch here is that the original US subscription is not automatically cancelled and there is no other way for user to see it unless the user logs out from all Amazon websites and logs back using "amazon.com" domain.
When month changes, Amazon uses only credit card number and expiration date to make the charges and to set Prime Video region, it won't use CVC or CVV code from backside of the card as it never asked it or use region set on Amazon website. This means they have to explicitly force their payment software to override all verification steps on the payment software for them to be able to proceed with the charge(s) and renew Prime Video subscription.
Normally this would be blocked by final payment processor who issued the card, but some issuers allow charges without CVV or CVC when it is considered recurring monthly payment even though credit card's terms of use states that first payment must always be backed up by two separate verification codes (for example using Verified by Visa).