Calpurnia's reading skills

Calpurnia taught Scout how to read and also her son (who is not a preacher). She is claiming that it was Miss Maudie's aunt who taught her how to read. I think that it's a little wrong. The thing is that Miss Maudie mentioned during the story that her family is not very found of black people. So, that supports my theory that she is not telling the complete truth. After the Civil war, there were no Jim Crow laws. But, white people would ignore blacks like if they were the garbage can. So, that is why i think she's lying a little.