Former Labor Secretary

I heard a talk by Robert Reich the other day. He was introduced as a former Secretary of Labor in the first Clinton Administration. Reich served as Labor Secretary from 1993 to 1997, so he is now a former Secretary of Labor. During the first Clinton administration, however, he was not a former Secretary of Labor.

I hear this shortcut all the time. A better formulation would be to state the office and administration, leaving out the word "former." Say, "Robert Reich was Secretary of Labor in the first Clinton administration." Or say, "Robert Reich is a former Secretary of Labor. He served in the first Clinton Administration."