Well, I don't think it's like an active check, but more like....
Okay. Let's say Dream World has a net. Each time you sign in to Game Sync, your game data (Specifically things like Pokedex information and whatnot since DW stuff has a direct effect on that) are sent through this net. Typically you can pass through no problems as you have nothing out of the ordinary. However, when you somehow have access to things like Zekrom's shiny form, even though it is unobtainable, your data gets caught in the net and is then rejected. It's sort of a passive method of keeping certain things out of Dream World since they may lack the ability to display them properly within the game itself.
Of course, that's just a wild guess on my part. *shrug*