Azrael,
I think what they figure is by leaving a higher stump the regrowth will be concentrated at the stump rather than suckers everywhere.
Then the natural pathogens can chase those roots down however when they meet the living roots of the nearby trees some resistance to the decay.
Could be an issue for a fungus like Phelinus Noxious which predominantly translocates via grafted root systems, you could very well be assisting healthy trees to contract a deadly fate.
About the worst up here for this problem is Chinese Elm (Celtis chinensis).
In this thread the tree died from it and there was a number of other dead stumps around same.
Diagnose this fungal death attack on Chinese elm (Celtis chinensis) Toowong Brisbane
I think the best course of action if using herbicides would be to sever the roots to adjoining trees. Like find the best place to do a cut like Mario says. Hit the tree with a good dose of round up, maybe a few days before removal too just to make sure but not too long before so all the leaves fall off.