For its ancestors to include both synapsida and diapsida, it would require interbreeding between wildly different species. Rather, it shares a common ancestor with both synapsida and diapsida.
However, it's true that it probably shouldn't be considered a reptile unless mammals are. Really, what we consider "reptiles" should probably be split into several different groups (testudines, squamates [possibly further split into squamates and sphenodonts], crocodilians, and dinosaurs [including birds]).