Keep your hands clean: You must seem a paragon of civility and efficiency: Your hands are never soiled by mistakes and nasty deeds. Maintain such a spotless appearance by using others as scapegoats and cat’s-paws to disguise your involvement.
Is there a connection to being on top and not having “blood” on your hands? I might suggest that without it, your underlings might perceive you as weak and antiquated. It may also be that as a puppeteer pulls the strings on his puppets, so too does the effective leader have henchmen to rough things up a bit all the while remaining pristine.