It didn't need to, that right is innate. As is your right to voice your disapproval.
She should be embarrassed.
By whose standard? Yours? Why should she care what you (or I, or pg, or Larry Ellison, or the wino standing at the corner of 3rd and Main) thinks about what should embarrass her? Or maybe she should worry about some abstract notion like "society" or (even worse) "polite society?" Feh...
I think we just have to agree to disagree on this point.
Fair enough. Reasonable people disagree all the time.
Anyway, I'll freely admit that I'm biased towards people who do things that go "against the grain" and break the "rules". If throwing a little profanity around and escalating a situation is their thing, I support it (to a point at least). I mean, I think there's a lot to be said for the mindset of "if I think this guy is being a doofus, I'm going to say he's a doofus, and damn political correctness."
Burning bridges isn't always a bad thing. And sometimes doing so enhances your reputation, rather than ruining it.
I'm betting a whole lot of people have more respect for Carol Bartz today, than they had yesterday, exactly because she spoke her mind, and showed some emotion and cut through the "PC" crap. At the very least, I know I do.
You can read about Ellison berating employees and screaming at them in a great book by Charles Ferguson called "High Stakes, No Prisoners". It's a wonderful accounting of building a startup in web 1.0 internet and selling it to MS -- Ferguson started Vermeer which built Frontpage.
See also, for example, Ballmer screaming and throwing chairs.
(Throwing chairs raises the "probably has issues" flag in any context that is not an Arnold Schwarzenegger movie.)