How "Mark Loose" functions in the "Skin Modifier"
The "Mark Loose" in the "Skin Modifier" only keeps Blender from drawing extra edge loops around adjacent edges of branch vertices (vertices with with three or more connected edges) in order to keep the output tight. With "Mark Loose" the previewed "mesh" of the "Skin Modifier" can stretch more widely between all adjacent vertices but moving the "loose" vertex still influences how the "mesh" volume is distributed as Jonathan also show in this video here. On the other hand, CTRL + A won't have any effect on a "loose" vertex.
See also the Blender manual under: