You guys are having this lengthy back-and-forth, when really all it boils down to is this:
There is no law preventing that chick from saying whatever the fuck she wants, whenever the fuck she wants. However, there are government-mandated consequences enacted on the entity that employs her when she breaks protocol. As such, her employer reserves the right to fire her for being a liability, or costing them too much money, or whatever else.
Being employed isn't a right, it's a privilege afforded to you. And if you want to continue to enjoy that privilege, you've got to play by the rules your employer sets. Some rules are out of their hands.
Can you imagine what sort of world we would live in if things WEREN'T this way? Companies would go under simply by making the mistake of employing someone who delighted in running their mouth off at all sorts of high-stakes public appearances. Why? Because apparently the government has no right to censor speech. But people who are offended by said speech tend to boycott related products. So the company is stuck with a bad-attitude employee who can't be fired because they're well within their rights to run their mouth all the time, yet people aren't buying the product.
There are other limits to free speech. You can't go into a crowded building screaming "FIRE FIRE FIRE" if there's no fire. It's the same thing.