We've thought about it, and now NoA president Reggie Fils-Aime confirms that it's true - along with downloadable demos, you'll also be able to download full games on your Nintendo DS via the Wii's upcoming Everybody's Nintendo Channel, which has already been released in Japan a while ago, but has yet to be released elsewhere.
According to the interview with New York Times, we'll see more DS and Wii integration, with a Professor Layton demo already confirmed. Exactly what the full games will be is unknown, and how in-depth they'll go also wasn't mentioned, though it's suspected that they won't be too hardcore as you might've hoped.
A problem with this format is the fact that the Nintendo DS hardware can't actually save data, meaning if you were to download something onto it, it'd be gone once you turned it off, which begs the question - will there be some sort of memory card that Nintendo will release alongside this? Let's hope so!