Like the mythical hydra, the Illuminati have many heads and even more hands. The minions of the Illuminati might work to their hidden master's ends without ever knowing the design of their work, or for whom they indeed work for.
Many games draw moral lines in bold colors, where the real world is not so easy to categorize. Suppose that the player characters are faced with an overwhelming foe? Even unsavory allies such as orcish barbarians may be better than no allies at all. More disturbing, these allies may be honestly friendly to the PCs when all is done, overcoming barriers of race and religion. Will the PCs remain friendly with the bloodthirsty humanoid tribesmen when their mutual foes are defeated? Some would expect the tribes to betray them, but after the characters have honestly won their respect, even orcs may not be all bad.