Lets get back to the definition of cancer stem cell: it's a cell which has the ability to initiate a tumour. So it should really be called a tumour initiating cell. It this respect it is more akin to an ES cell. ES cells are destroyed in the process of forming a human being. Conversely adult stem cells cannot form an organ, but they are needed for tissue homeostasis. These properties are, I think, what most people imagine a cancer stem cell has. It's the replicative compartment of the tumor.
This leads to an ambiguity: is the tumour initiating cell the same as the tumour homeostasis cell?
Take these facts into consideration:
-Many tumours only grow in the periphery and have a necrotic core, does it mean tumour homeostasis cells always migrate to the periphery, or are self-renewing at a high rate on the exterior. Would the explanation that any cancer cell in the periphery has a probabilistic ability to act as a homeostatic cell be more parsimonious?
-The authors suggest that normal cell lines have much lower abilities to form tumours than their "super" cells. They say it usually takes a million cells in a xenograft versus as little as 100 of their cells. So they argue that only about a cell in a million can hold the proliferative potential of a cell line. We know that's not true, all the cells are dividing, and you can easily start a new culture flask with 100 cells, I've done it countless times. The limiting factor here, I think, is the ability to implant and survive in the hypoxic and growth factor poor environment of a mouse, after having lived in the easy condition of growth media.
-Finally the authors argue that their media selects stem cells. Obviously that's not true, otherwise both culture conditions would create the same tumours but at different rates depending on the selection stringency. Here they get 2 types of tumour. More likely they've either selected for two types of cells or changed the phenotype of the cell with their media. They do acknowledge they have two cell types, but they argue that they have enhanced stemmness, when all they show is they have a different cell with a different probabilistic ability to initiate a totally different cancer type.