No one can fire a federal employee except a supervisor of her/him. The lady was hastily "removed," and just as hastily re-hired, and even more hastily deified. She is more famous, more powerful, more widely known and very likely wealthier than she was a month ago. No one thinks badly of her: naming her politics is not an insult, just as calling anyone anywhere a "socialist" is not an insult.
There was much sloppiness here, and plenty of blame to assign. Even the very organization to whom she spoke condemned her. How is that for stupidity?
Your focus on one media organization is perhaps the major reason why a responsible left in the US remains a fiction.