No. I understand where she's coming from in terms of people being able to speak, but I believe that she's confusing two things. Free speech is a right held against the government. If you are allowed to speak—that is, the laws don't prevent you from speaking—but somebody else hears what you say and acts accordingly—for example, let's say that you lose your job—then that is not a free speech issue, because you don't have a right to free speech against your employer. It has nothing to do with free speech.
People on the left, if I can put it that way, are fond of saying that you have rights, but there are consequences to exercising your choice. This is one of those consequences. If you choose to say something—which you are free to do—and somebody else decides that they don't like what you said, then they are free to respond as well.