you are correct. If the database entry is simply Agave parryi, any photo of Agave parryi would be a correct entry, but if there are separate entries for some of the var./subsp. it seems strange to not be taxonomically correct and have them all. Effectively they have separate entries for subsp./var. neomexicana, couesii, huachucensis, and parryi, so really the main one missing is truncata, which may overlap with subsp./var. parryi, but does have a distinct geographic location of occurrence compared to all the other varieties/subspecies.
I find it interesting how Starr downplays the distinctions - I am sure that in the areas where the ranges of the different varieties/subspecies overlap that things get muddled, but if you look at pictures of the different var./subsp. from say the middle of their range, the differences between the plants are pretty clear. Check out the gallery entries for the parryi's at Agaveville.org and you'll see what I mean.
I am willing to help try and get things sorted out, but it seems the process of getting pictures moved here is somewhat involved and I am by no means an expert - the only A. parryi I have successfully kept alive has been var. truncata, I lost a beautiful parryi subsp. parryi last spring due to the wetness, I wonder about the entry in the database that suggest they grow in mesic and dry mesic conditions... maybe if they are in super well draining soil, but to me this is a plant that really wants to be dry.
I have var. huachucensis but I have to see if take on the distinct shape of that plant before I trust the ID on that plant. I also have var. couesii but also with some doubt about the positive ID, that plant is still small and growing very very slowly. I am looking for a neomex plant as those in my opinion are the best looking subsp. of A. parryi.