Ok, are there any third parties that have written about the MLK story? Any mention of it in one of Shatner or Nimoy's books, or other books by or interviews with any of the other cast members, producers, or staff?
I would think that, if this story were true, the first thing that Ms. Nichols would have done would have been to immediately tell it to everyone that would listen, which would have included Shatner, Nimoy, Roddenberry, and the dozens of other people that she interacted with on a regular work day at the Trek set.
To put it another way, let's imagine that 10 years ago I had met Steve Jobs, one of my personal heroes and inspirations. I would not have waited until now to tell my geeky friends and coworkers about the most awesome thing that ever happened to me.
Count me as someone that really wants the story to be true, but it just doesn't seem to be, unfortunately.