I guess the quote was a bastardization of another MLK quote.
Apparently, here is something he actually said:
"The ultimate weakness of violence is that it is a descending spiral, begetting the very thing it seeks to destroy. Instead of diminishing evil, it multiplies it. Through violence you may murder the liar, but you cannot murder the lie, nor establish the truth. Through violence you may murder the hater, but you do not murder hate. In fact, violence merely increases hate. So it goes. Returning violence for violence multiplies violence, adding deeper darkness to a night already devoid of stars. Darkness cannot drive out darkness: only light can do that. Hate cannot drive out hate: only love can do that."
MARTIN LUTHER KING, JR., Where Do We Go from Here: Chaos or Community?, pp. 62–63 (1967)
The first part must have been made up and added onto his quote and it somehow spiraled. Like a game of telephone. Sorry to misquote. Who knew this thing called the internet could be liable to misinformation?