I think an exam is a bad example of "right answer" being important. Your grade depends on getting the professor's preferred answer, even if it's wrong. Cases where you want the right answer are things like letting your child play on a raised deck that you built, or eating food that you decided was "probably good" after being left at room temperature for a while.
While I agree with what you've factually said, I think the post was aiming at times people instinctually understand they cannot argue a better answer. You've surely seen people build unsafe things and then try to argue that they "should have" worked, so arguing to that likely won't convert anyone, but the author found resonance in the example of school exams.
Again, I totally understand and agree with you about the whole "guessing the teacher's password"-related bit.
My point was that we're talking about getting the best answer assuming the professors also know the best answer. I feel like it's nitpicking to go around diving deep in arguing about the assumptions. The point of the article still stands.
For what it's worth, I, @tomcatfish, was agreeing with you, @ship_shlap, in general, while also stating that I agree with @Dagon.
I don't think even Dagon was disagreeing outright with you, more noticing that if they expand your metaphor one more step it stops working for them. It's pretty important when using a metaphor to note when it breaks down, and I actually like your point a bit more with their clarification because I can understand the full shape of your point a bit easier when I know what assumptions I'm meant to use.
The point of the article still stands for me too!
It's quite common to see people bending the truth if it works for them. It happens far more often than you'd like to think. For example, seeing the weak point of a belief but you choose to ignore it and rehearse the strong points. What's the harm in that?
What if the setting changed - You're in an exam in university, and your GPA depends on it. Your degree demands a GPA of 3.7 (or something). You'd definitely want to attack the weak parts of your answer. It would be so much more relaxing to ignore your large possibly-wrong answer. But no matter how much you defy the universe (haha I don't care I'm too tired or I'm too lazy, why don't you make me correct it), you'll get a lower score. When the setting becomes an exam, you'll have to start correcting all possible mistakes.
Life is that exam, and you will face the consequences for having incorrect beliefs. Treat your beliefs the way you treat your answers on an exam (Except in real life you should be rational out of curiosity, not out of duty, of course).