You are equating "a shadow" to "Shadowy Illumination".
The first is not a game mechanic. The second is.
If HiPS was written "Hide in Plain Sight (Su): A shadowdancer can use the Hide skill even while being observed. As long as she is within 10 feet of shadowy illumination, a shadowdancer can hide herself from view in the open without anything to actually hide behind. She cannot, however, hide in the shadowy illumination of her own shadow.", then I would agree with you.
I think the "can HiPS next to the color green" is a good example. It does not matter if the viewer can see the green or not, it is merely important that the color green be there.
Let's take a different example:
PC1 is holding a lit torch in front of him (not above his head) and is walking in a very large totally dark cave.
PC2 is walking 5 feet behind PC1.
PC2 is in PC1's shadow.
PC2 is not in shadowy illumination (at least according to most DMs) and would not get a concealment miss chance if a goblin fired an arrow at him from the darkness over 200 feet away.
In order for you to rule that Shadow = Shadowy Illumination, you would have to give PC2 a concealment miss chance in this circumstance. I know of no DMs who do that in their game (i.e. keep track of light sources and whether PCs are standing in the shadows of other PCs).