There is no telling if The Captain would have accepted when the typhoon was going on. Also While again if they would have accepted Queeg offer of in the briefing room Queeg a sick man still had no business running a ship. He was ill and while his past service is admirable and greatly appreciated Barney the lawyer made a big deal over nothing at the end.
I think the point he is raising...and I agree with him...is that Barney seems to think that because Queeg worked long and hard prior to the war, eventually rising up to command of a vessel, he deserves some sort of "pass" when he screws up and the other officers should, in a way, cover for him.
I think Barney was wrong. Especially in war time, having an officer in charge of a ship who, for various reasons, cannot handle the stress, freezes up, and cannot make a decision is dangerous.
Now, had the other officers been more co-operative with Queeg it might have delayed his breakdown a bit in a crisis, but it WAS going to come out sooner or later and most likely with very bad timing. How would Queeg have reacted during, say, a Kamikaze attack?
Having said that, I'm not questioning the effect of Barney's speech as a piece of cinematic drama. It's excellent and helps make the movie a classic. I'm only commenting on the idea he promulgates as something the Navy should follow as policy in the real world.
It was made clear in the novel that Queeg was not mentally ill and that his opposition to Maryk was defensible, according to an expert witness in ship handling. He was well meaning, but with an unpleasant personality. Willie Keith, in the novel at least, concluded that the officers should have been more cooperative with Queeg and that the mutiny was wrong.
The theme of The Caine Mutiny is Accountability, and how the mark of a man is how you address it. A man accounts for his actions, right or wrong, and bears the consequences for them.
Throughout the novel, especially, every officer associated with the Caine dodges accountability. Queeg effectively is forcing it on them in a very haphazard and blunt manner, but he, especially, dodges it at every opportunity where it reflects negatively on him. He blames his officers for his own failures, lapses of judgment, and irresponsibility. He also uses blackmail and extortion to get the outcomes he wants (especially during the Stillwell Court Martial), and he certainly doesn't inspire loyalty from anyone.
That being said, however, watch how Keefer dodges his own accountability regarding recommending that the Captain is insane. It wasn't that Keefer didn't believe in his assessment, it was that he was afraid of Article 186, that he might be held responsible for conspiring in a mutiny if things do not go according to plan.
Maryk dodges his own accountability to the Captain, and even goes through the motions of satisfying Queeg's ravings while at the same time trying to keep a lid on things. He isn't loyal to Queeg anymore than the others, especially after the Yellowstain incident.
Barney was right about the Caine's officers, especially about Keefer, but all this was meant to do was to teach a lesson in Accountability. That whatever you do in life, do it with the character of conviction in your heart and mind, right or wrong, that whatever you do you will suffer dire consequences even if what you did was the right thing.
If you read the novel, Keith's relationship with May Wynn was struggling because Willie could not assure May that he truly wanted to be married to her regardless of what his mother thought, and that their relationship would never be tarnished by whatever his mother thought or did. She didn't want to be a trophy, or someone to be pitied, and Willie had to learn to be Accountable.
In the end of the novel, Willie doesn't marry May. She's in a relationship with a band leader. He's the last captain of the Caine, taking her to be torn down into scrap, but he decides to marry her after all, knowing that it's going to be a very tough battle.
IIRC, in the book, most of the officers are reservists who perhaps were a little more 'independent' thinkers than regular naval officers. They'd become used to the more relaxed routine of De Vriess (which had not had such an adverse effect as was hinted at in the film - they generally hoisted out and retrieved minesweeping equipment faster than any other ship in the flotilla, for example). The point was that Queeg was the wrong choice to take over what had been a fairly well-run - and happy - ship. That doesn't mean to say that the officers were right not to support him, but the book does give far more examples of Queeg's tyrannical behaviour than we see in the film and, although it's been a while since I've read the book, I don't recall any instance of Queeg holding out an olive branch to the officers. However, the book does make the point that it was Keefer who was the ultimate instigator of the mutiny - he emerges as a far less sympathetic character than Queeg in the end.
Barney was right about the Caine's officers, especially about Keefer, but all this was meant to do was to teach a lesson in Accountability. That whatever you do in life, do it with the character of conviction in your heart and mind, right or wrong, that whatever you do you will suffer dire consequences even if what you did was the right thing.
ac·count·a·ble/əˈkoun(t)əb(ə)l/ adjective 1.(of a person, organization, or institution) required or expected to justify actions or decisions; responsible. 2.explicable; understandable.
Only kangaroo courts, or courts in systems with perverse laws, when presented with all the pertinent information, punish people who did the right thing.
Barney himself subverted a system (a court martial) and effectively got Queeg punished (in his eyes apparently unjustly) to get his client freed, even though he thought his client apparently to be an accomplice, of moral if not legal culpability, to the person with real guilt, Keefer.