The reason the VED might matter abroad is because it gives them an idea if the car has been in the country over the prescribed legal limit which is a maximum of 6 months in any one year. If the VED is not paid, there is a very good chance the car does not have a valid MOT, which means the car does not have valid insurance and has been there for longer than allowed. The Spanish especially are red hot on this and have been for around 10 years as it allows them to levy spurious fines and charge (illegal) importation fees and impound fees for overage vehicles.