The US is approximately 10 years behind the rest of the world on this, and many US bank cards have not been usable in Europe for a long time.
The liability only rests with the person taking the card as payment if they don't have a PCI compliance certificate. I managed to get mine about 5 years ago, limiting my liability to £15, and then the next Jan 1 Visa told me my merchant charges were going to double so I told them to come and collect their machine tomorrow and I stuck to paypal ever since.