I'm not outside looking at my Pathfinder, but I "think" what they mean is there's not enough clearance in the wheel well for the chains. You wouldn't want the chains to hit all those plastic pieces...especially when you turn.
I agree theres not alot of room when the tires are turned. You can use snow cables that are smaller and I think work better than chains on passanger cars. Theres only one way to realy find out is by putting some on. If I remember correctly theres a topic on this all ready.