No, Ashtagon, this is not what is stated in the ability's description. The Shadowdancer's HiPS ability reads:
"Hide in Plain Sight (Su): A shadowdancer can use the Stealth skill even while being observed. As long as she is within 10 feet of an area of dim light, a shadowdancer can hide herself from view in the open without anything to actually hide behind. She cannot, however, hide in her own shadow."
This is a statement in three parts:
1) "A shadowdancer can use the Stealth skill even while being observed." This is a sentence which stands on its own and does not stipulate the use of shadow or anything else. The Shadowdancer can simply use the Stealth skill (with all the normal ramifications of using that skill) while breaking a single rule for that skill - namely, you normally need to be unobserved to use it, or create a diversion to hide, which part the Shadowdancer can ignore.
2) "As long as she is within 10 feet of an area of dim light, a shadowdancer can hide herself from view in the open without anything to actually hide behind." There is no reference to opponents' sensory capabilities here. "Dim light" is a condition that can objectively exist in the game world, irrespective of the presence or absence of creatures which may happen to be affected by it or not.
Note that normally, you need concealment or cover to use the Stealth skill to hide. Further note that normally, dim light is one condition among many that affords concealment (fog would be another, a Blur spell another, and so on). So normally, a character can use the Stealth skill to hide within an area of dim light
Creatures with darkvision would, however, not be affected by the dim light: against them, it doesn't provide concealment, which is the sole reason you cannot hide from them if there's only dim light and no other condition allowing hiding.
However, Shadowdancers get to break not only the "must be unobserved or create a diversion to hide" rule. They also get to break the "need concealment or cover to hide" rule. They can hide whenever there's an area of dim light within 10 feet. This is totally independent of the question whether said area of dim light would be enough to afford them concealment. See, Shadowdancers don't need concealment - they only need dim light (which accidentally also happens to provide concealment vs. creatures without darkvision, but that is beside the point here). For this reason, darkvision or the lack thereof has no bearing whatsoever on a Shadowdancer's ability to hide. Shadowdancers need dim light to do so, period.
[Ironically, by RAW, they can't hide in total darkness. Funny though, that.]
3) "She cannot, however, hide in her own shadow." This is a clarification of the second part and has almost no in-game ramifications as long as you have any disposable object on your person that can be thrown to the ground.
So far the rules. How you flavor it in-game is your own decision, of course, but a lot of D&D publications hint that shadow is considered a substance, "shadowstuff", that can be molded and shaped if you have the magic to do so. This is what Shadowdancers do IMO, but whether that also holds true in your game doesn't influence the logic of the rules discussed above.
Finally, somebody mentioned the Ranger's (Ex) HiPS ability. That ability reads:
"Hide in Plain Sight (Ex): While in any of his favored terrains, a ranger of 17th level or higher can use theStealth skill even while being observed."
Note how this differs from the Shadowdancer's ability: it only duplicates 1), but not 2), and even that only in certain kinds of terrain. This means that a Ranger still needs something to hide behind (cover or concealment), unlike the Shadowdancer. If a 17th level Ranger tries to hide in an area of dim light, creatures with darkvision will still see him!
Magic blows mundane out of the water once more.