The Catalog of Life is wrong. I will be happy to make a separate comment about this. Here is the history of the plant var. truncata as I understand it. The form most commonly encountered in cultivation is a descendant of a plant that Howard Gentry collected in 1951 and deposited at the Huntington Botanical Garden. In his landmark agave book Gentry broke down the species parryi into varieties huachucensis, couesii, and truncata. These are the same varieties that apply today. With the inclusion of ssp. neomexicana the species Agave parryi gained ssp. parryi (used to describe the plants originally constituting the parryi species). The 3 varieties he described have been recognized by both subsequent books on agaves (by Irish and Starr). They are distinct from each other and have been since Gentry described them.
For this reason Agave parryi truncata is not and has never been a synonym for Agave parryi ssp. parryi, among the people who have grown the plant. It is a type of parryi ssp. parryi, nothing more.
This is a database error. I would invite Thijs or other growers of the plant to chime in with their experience and sources.