I think net caloric burn (that is, total calories burned subtracting the calories you would have burn over that interval regardless of motion) for covering 1 mile distance tends to be pretty static at any one specific weight. Once you go from walking to running, the pace becomes irrelevant in the calculation of net caloric burn, which I think is the number the kg/km rule gives (it predicts a 150 lb person would net a burn of 110 calories running 1 mile, which is fairly accurate)
I am fuzzy on this stuff so I might be mistaken, but I think that is the distinction that supports Sprint Geezer's initial premise.