No the rug doesn’t attribute the quote to Dr. King or anyone else. The problem with the story is that those are King’s words. He paraphrased Parker’s (distant relative of mine)much longer quote
The original said: “I do not pretend to understand the moral universe; the arc is a long one, my eye reaches but little ways; I cannot calculate the curve and complete the figure by the experience of sight; I can divine it by conscience. And from what I see I am sure it bends towards justice.” This is from his 1853 sermon Justice and the Conscience
That’s the original source but it’s different from Doctor Kings words when he paraphrased it: “The arc of the moral universe is long, but it bends toward justice.”
If so, it's a LEGITIMATE quote of MLK....who was obviously paraphrasing a great thinker.