I agree 96.9% with your last statement.
While I have no doubt the CFACC sent you precisely because he believed you had the skills and ability to unf**k the situation, I doubt he "screamed" it at you in a large public forum. I also suspect he selected that phraseology because he knew you, and your leadership/management and followership styles, and knew you would read him as he intended: "loud and clear."
I worked with the CFACC, C3 and DIRMOBFOR in the beginning of OIF and never once heard any them utter an angry f-bomb in a public forum. Their demeanor and use of language set a clear, professional military tone and I, for one, appreciated it. There are few words in the English language that we can use like an f-bomb--it's versatility is unsurpassed. But, I think it's still vulgar and coarse, and I prefer to keep my military bearing intact and have only once myself uttered an f-bomb in flight (several "holy sh*ts!, though).
Your tale of screaming at the SNCO may have been exactly the right motivational tool to use at that moment: you needed to get a certain message across and you chose that method/language to deliver it. Maybe it worked exactly as designed, and maybe the SNCO believes to this day that you are an unprofessional, angry tool who laughs about the incident now because he's afraid if he doesn't you'll do it again. I'll never know, and neither will you. But, even you would have to admit that, viewed by a dispassionate observer, your rant would appear as a childish, hot-headed, emotionally-charged (irrational?) outburst. I'm not saying it wasn't effective, but I'd hope that a professional air-warrior would normally not choose to salt his communications in that way.
Like the senior leaders I served with, I want my bosses, crews, staff, airmen, and peer officers I work with to believe I keep my cool under pressure, use rational, dispassionate reasoning to reach the right decision, and never get "ruffled" or "out-of-control." I think indiscriminate use of the f-bomb destroys that image and does not instill in them confidence in my ability to lead my troops or my crews, in combat or back at the home-drome. Perhaps that's what happened to "Captain Bligh?" Her superiors lost confidence in her ability to lead in part because she wasn't cool, calm, collected, and in control in difficult situations?
In the end, I like to think that as an officer, I should act the part--that means no f-, c-, b-, or any other kind of bombs while in uniform. I try not to raise my voice--though I do "change my tone" when the situation calls for it. While I disapprove of such vulgarities and usually counsel (in private) my younger troops with a speech similar to this one, in the end, each of us will lead in our own way.
If what really matters is getting the mission done, regardless of professional demeanor, couldn't it be said the female skipper did exactly that? And look what happened to her...
Fly safe!