Fans of Dr. King and Gandhi tend to gloss over the fact that they realized that non-violence would work precisely because those in power were not living up to their own Judeo-Christian/Anglo-American ideals. Where those ideals do not already prevail--where the Bible and Madison and Magna Carta and the Declaration and Edmund Burke and the rest are not the basis of the society--non-violence is a recipe for self-annihilation. Recall that Gandhi counseled the Jews to go willingly to their doom to teach Hitler a moral lesson.
Likewise, it was when Dr. King departed from Anglo-Americanism, when he began to insist on equalitarianism of results rather than equality of political/moral standing, that the movement he led lost its credibility. He took his power from the ideas of his culture and lost that power when he moved into opposition to that culture.