Wow, a great recommendation, Yahtzee. LittleBigPlanet is perfect for a new gamer; visuals welcoming enough to draw in a casual player with depth that can cause them to sink hours into it. And, on that point, I somewhat agree with your argument of Mario not really fitting the casual description. I've seen kids losing their mind trying to beat a single level of, not only the Galaxy games, but also New Super Mario Bros. Wii. You have no idea how angry these kids can get when they bounce off each others' heads and fall into three separate pits.
Hell, I've even had some troubles trying to get some of the hardest stars in the Galaxy games. LittleBigPlanet by comparison just lets you go through the levels and appreciate the fine work that was put into it. Plus, the co-op aspect is great in the way that you've mentioned it.
On a similar note, I think that Rock Band 2 serves as a good starting point. Not that it teaches you valuable game tactics. It's because my experiences have taught me that a four-piece plastic band armed with a few hundred songs (counting those that you download) can give a positive view of gaming culture to those who weren't particularly partial to begin with. Just for the fact that it serves as a fun way to use games in a more friendly manner, this is a good starting point for anyone curious of the culture. (In addition, easy mode plus no fail means that anyone can jump in on the game.)