I run the 13X6.5's all around on 8" rims, they do well for me. The wide rim really pushes the side walls out and they refuse to "Roll Over" My thought is this, If I stand straight up with my heels and toes together, you can push me over with one hand. If I spread my legs out 3 feet, it's very hard to push me over.
But I have seen people run very well with a narrow tire. A lot of it is your driving style.