Ripped, I don't think she's saying that you have to be a black woman to tell a black woman's story as much as that you need to listen to black women's perspectives to do so. She cites Caroline, or Change which was written by a white man and a white woman and directed by a black man. And with regard to Mother Courage itself, she cites Kushner's translation as being something of a gold standard.
I saw this production before this all happened, and that is making me particularly sympathetic to Pinkins. The decision to set it in the Congo is tacked on at best, and the version of the script being used is really terribly chopped up. Mother Courage is an extraordinary play, but you would never know that from what Kulick has put on stage. The setting could have been almost anywhere except for the fact that the posters and program repeatedly told us that this was the Congo. So it felt like an afterthought at best, cultural tourism at worst.
CSC's Caucasian Chalk Circle was, to me, also a terrible production that a strong cast couldn't come close to saving. Kulick hasn't demonstrated a decent sense of how to approach Brecht. Add in the numerous issues with race and gender here, and to me it is understandable that an actor could reach a breaking point.
Could this his have been handled better? Absolutely. But I appreciate Pinkins' passion and her commitment to doing worthy work.
I also took her comments about her talent not matching the material since Caroline less as an indictment of the other plays she has done than a comment on the roles--Caroline and Courage are both extraordinary parts that would call on an actress to deliver on numerous levels and pull from their deepest reserves of talent. So to me, I don't think she was saying that she is "better than" Radio Golf, the example used above, as much as the part she played not asking as much from her.