But that is not a viable answer to the question. The brilliance of the scene is that Jessup is caught (from the very beginning) in a dilemma - and he can't have it both ways.

Do you recall the Kaffee outburst? "I WANT THE TRUTH!"
At that point, Kaffee is all-in. The words themselves imply that a highly decorated Marine commanding officer has not been truthful in a court martial. Without a single shred of evidence to support the implication, Kaffee has violated a code of conduct that he has been informed of and aware for quite some time. If his bluff using the airmen as bait does not hook Jessup, Kaffee is toast.
Fortunately for Kaffee, Jessup has a character flaw in that he cannot stand the fact that he has to sit there and answer to someone in a 'gurly white' uniform who has never stood a post or commanded combat troops. Therefore, in spite of the fact that he has conspired to allow two innocent Marines to take that fall for a murder they didn't commit, he feels compelled to put this little pipsqueak sailor in his place. How dare he question my methods of command!
"Did you order the code red?"
"DAMN RIGHT I DID!"
Game over.

I personally am a fan of "what if"s. As a kid I always wanted to know what could have happened instead, or what might happen after the ending. Anyway, on to my reason for commenting. The dialogue might be a little convenient, but to go as far as to call it lazy writing does a disservice to all the character development established earlier in the film.
Colonel Jessup's actions and attitude in Cuba serve to set him up for this very moment. They establish in his scenes that he's quick to anger and overreactions when challenged or confronted with a point of view he doesn't agree with. Look at the scene where the officers discuss whether or not to transfer Santiago. Colonel Jessup is annoyed, and because of that he gets carried away and mockingly calls in a soldier to order the entire division to surrender. When Markinson questions his decision it angers him, so he not only asserts his control and authority over the situation, he intimidates and asserts dominance over his friend. Later, when Kaffee is at lunch with Colonel Jessup, it is established that Kaffee is capable of getting under Jessup's skin. It's also established that the colonel will say inappropriate things, what you could consider misconduct, when he essentially sexually objectifies Demi Moore's character. He says it because he's absolutely certain that he can say what he wants.
They teach you two quite important things about his character; first that he's an emotional man with a short temper who figuratively attacks those who challenge him. The second is that he's built up what is essentially a God complex. He does the correct thing always, refusing any advice or criticism. He knows what's best for everyone, thinks he's more worthy of respect than anyone else and has found himself in a position of ultimate authority. In Guantanamo, he may as well be God.
So Jessup thinks he's infallible, untouchable and justified, and he has a short temper to go with his ego, making him prone to outbursts (sometimes saying things a person of his position should know better than to say). Just the kind of person who would break in that courtroom. And look at how he reacts when he's arrested; he not only thinks what he did was right, he genuinely is surprised that he would be arrested.

Thank you for proving my point. Well done! And no I didn't miss the point. It was too easy ergo lazy writing. Deal with it!!
We have to show the world that not all of us are like him: Henning von Tresckow
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To be honest that's something a patronising ass would say.
To tell you the truth, that's something a total dimwit would claim, because of missing the whole point.
Memory is a wonderful thing if you don't have to deal with the past

he couldn't have answered any differently than he did, because this was a movie (with tailor-made dialogue) rather than real-life events.
To be honest that's something a patronising ass would say. The OP is well aware it's a movie and not real life. Also he raises a very good point. Kaffee caught Jessup out far too easily. Don't get me wrong I love the movie for it's drama but that scene is far too contrived to the point of lazy writing.
We have to show the world that not all of us are like him: Henning von Tresckow
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he couldn't have answered any differently than he did, because this was a movie (with tailor-made dialogue) rather than real-life events.
The value of your question is in similar analogy to, say, "what if Kaffee was run over by a car on his way to court prior to putting Jessup ob the stand? How could then the truth get out in the open? Hmmm?".
So I'm asking you now, why should the script's author pull the rug under his own feet, by twisting the plot in this manner?
Movies aim to entertain an/or make points (apart from making money of course) and this movie served no other purposes than the aforementioned, so do not trouble yourself with such a pointless "what if" like the one you proposed.
Memory is a wonderful thing if you don't have to deal with the past