No it isn’t a lie. Thompson voted for the DOMA which defines marriage as being between one man and one woman. Now he proposes an amendment that defines marriage as any crazy thing the states define it to mean. That’s a flip-flop on his part.
Aha. Federalism is great until you think it won’t do what you want. Tsk, tsk, tsk.
Have you actually ever read DOMA? The Defense of Marriage Act (DOMA) does two things. First, it provides that no State shall be required to give effect to a law of any other State with respect to a same-sex "marriage." Second, it defines the words "marriage" and "spouse" for purposes of Federal law. This is exactly Fred Thompson's position. For Federal purposes marriage is between a man and a women. States are free to define marriage as they want but no state is forced to accept same sex marriages from other states.
Thompson has had a consistent position based on federalism and states rights. He voted for DOMA because it is consistent with his position. No flip flop.