A few minor details at a time,
but over thirty years, those minor details turn into one helluva whopper.
It started with her thinking "What would MLK do?"
It's now evolved into Dr. King personally delivering a version of the "I Have A Dream" speech, which has also gotten longer and longer each time she tells the tale.
That's not just "a few minor details".
It should be noted that this is not the only instance where she's gilded the lily while relating a tale. Her version of that scene in ST IV where Chekov and Uhura are asking passersby the location of the "nuclear wessels" and the lady out walking her dog tells them Alameda is in stark contrast to the versions told by both Walter Koenig and Leonard Nimoy. In Nichelle's version, they went through multiple takes, the lady wasn't supposed to say anything, but kept chiming in "because they seem so nice", eventually leading to a minor conference where Nichelle suggests they just sign the lady to a one-day contract so they can use the footage and move on.
Koenig and Nimoy, on the other hand, only tell of one take, and that the lady wasn't one of the extras, but someone off the street who was just walking her dog, had no idea there was a movie being shot, and was giving directions to these two strange people. The moment was so humorous and honest, they knew they wanted to keep it, but now it was a mad dash to track her down and get her to sign a release so they could use the footage.
And we're not talking thirty years of failing and/or revisionist memory in this case, this started within a few years of the movie.