stolen identity doesn't usually mean that someone has convinced a government office that they are you, that would be a lot harder for the reasons you say. It's

stolen identity doesn't usually mean that someone has convinced a government office that they are you, that would be a lot harder for the reasons you say. It's more often someone having enough information to open a credit card in your name and start using it, or take out a loan—things for which the government is not really involved.