And just to add to the confusion of those used to a different system, we're technically required to pay sales tax on out of state purchases. In theory, a NY resident traveling to EU would get back the VAT and then owe NY any applicable sales tax (less sales tax paid at time of purchase).

NY has attempted to enforce this for US out of state purchases - they get records from shipping companies, etc. They even at one point sent revenue officers to write down NY auto license plates when parked in the Ikea parking lot in NJ.