The flash and pedigree refers to one of the ways you can convince people of your expert knowledge. People tend to put more faith into a recommendation that comes out of a Harvard grad than others, even if the Harvard grad talks completely out of their ass (pedigree). Furthermore, if the client sees that other people, just like themselves, have been paying this Harvard grad to talk out of his ass, they figure he must be a good person to have (prestige).
So in essence, the high rate of consulting comes down to the ability to say 'but we have lots of Harvard/Princeton/Yale minds working on this!' and 'No one ever got fired for using IBM'.
And that's just the way the firms like it.