Never owned a KS and only have known one person who said they have owned one.
But in general yes the skinny barreled Model Seven is an accurate rifle. I have one of the originals in 7-08 that was never much better than a 1.5" to 2" rifle until I shot some Hornady Light Mag ammo in it. For the first time since I got it that rifle was turning in groups under an inch at 100 yards.
Now that lack of accuracy has never matter cuz when I used it then my oldest son and now my wife using it that rifle has never missed game and never required a second shot on any animal and a LOT of them have been taken with that rifle.
All the rest of the Model Seven's I've owned have shot at least some loads under an inch when I did my part. None of them ever provided me with an excuse as they've always done fine at the bench and in the field.