Nichols recollects that during a promotional trip to Memphis, an assistant told her that a fan wanted to meet her.
Listverse: 10 Things You Probably Didn't Know About Star Trek
The chance encounter occurred at an NAACP fund-raiser held the day after Nichols…turned in her resignation.
Times Daily/Friday, Dec. 13, 1996
At one of her regular meetings with with civil rights leader Dr. Martin Luther King Jr. -- she helped at fund raisers and he was her mentor--she told him she was thinking of quitting.
Anchorage Daily News - Aug 17, 1989, p. 21
"[MLK] was a close friend, and he happened to be a big Star Trek fan," she says…
The Afro American, Dec. 8, 1979
Did some searching via Google News and Archives and hit the stories above. They're not consistent in their details ("chance encounter" vs. "regular meetings"), but they do all claim she met him, going back to at least 1979. If there are indeed printed stories in which she says it was a phone call or something else, I suspect it'd be pre-TMP.
Well done! Thanks for the research. However, the Afro American interview from 1979 doesn't state that MLK told her face-to-face. All we know from that interview is that he "told" her. I guess we can assume, because she claimed he was "a close friend," that the conversation was in person.