Kroil is not gun oil. It is alleged to be a penetrating oil, which has the viscosity of kerosene. And really, in my opinion, it is no better than simple kerosene as a penetrating oil. I will never waste my time using Kroil on a stuck gun screw when I know there are much better products. But that's another discussion.
I agree that there will always be incidental contact with the (correct) thin film of gun oil where barrels contact forend wood, etc. But the real problems we see with excessive oil getting into stock wood is mainly where it creeps out and soaks into end grain. The best way to prevent that is to apply a very thin film of gun oil which isn't likely to flow downhill. If uphill oil creeping was the problem, then it wouldn't matter how guns are stored to prevent stick oiling. People who lay it on that heavy would be better advised to do it properly, or remove their stock wood and store it separately.
I'll bet there are guys that store guns barrels down in their gun safes who literally have puddles of gun oil on the floor of their safe.
