The concept of the height of a Dune is indeed based on who is defining the "height". At Great Sand Dunes, they measure the height of the taller dunes like Star Dune and High Dune based on the elevation of the lowest continuous leg of that dune vs. the elevation at its highest point. The dunes are generally considered to be about 700 - 750 feet tall, but they would be "taller" if you chose some sandy spot down on the gradually-sloping valley floor to be the starting measuring point.
A simpler statistic -- and one that isn't open to nearly as much interpretation -- is the elevation of Great Sand Dunes. A claim that they are the highest (in elevation) Dunes in the U.S. is much easier to explain than the claim that they are also the tallest (dune base to dune top) in the U.S.