Now there is no freedom of speech as it relates to private organizations, however by violating their own rules (the CHoI) they are guilty of defamation, false light, and libel for falsely accusing her of several things. If this affects her ability to perform her job (as a civil rights lawyer) or has other negative impacts on her they can and should be held responsible.
BTW, in cased you missed it, the LDS church was caught lying about her and the role of the leadership in SLC in her excommunication.