I listened to the interviews last night. The first is the MLK story. She said that she joined Star Trek as resume-filler for her hoped-for theatrical aspirations, and after the first season she'd been offered a promising role in a theatre production and decided to leave to follow that. However, while attending a NAACP meeting MLK asked to meet her and stressed the importance of her role as Uhura, after which point she went back.
The second interview is about her work with NASA, including recruiting women and "people of color".
Yep, that's 'official version 3'.
Version 1: She received a letter from MLK.
Version 2: She received phone call from MLK.