I've always thought my swing stance might be a little too wide too. But honestly, it almost has to be as wide as it is. It's not crazy wide, maybe 3" outside of the shoulder on each side. If I'm keeping the bell pretty high between the legs, I have to make the space for it - especially for the 32kg.
So, the feet may look wide, but if you pay attention to the space between your thighs vs. the size of the kettlebell, it makes more sense.