[Pedantic mode on]
The Wii is actually designed to make use of an internet connection, for online gaming, shopping for downloadable games, sharing Miis, obtaining the latest news and weather updates, and for the Opera-powered "Internet Channel" web browser. Internet capability is actually a selling-point on one of Nintendo's in-store promotional videos. "The Wii will revolutionize the relationship between your home, the TV, and the Internet."
In general I agree with the point you were making, but you were a tad off with that one detail.