Both Captains' unwaivering confidence. Is it believable?

Was it believable that both men were so confident in their ways that they were willing to draw guns on each other multiple times during the event?

Put yourself in Frank Ramsey's shoes. Your chief of the boat doesn't support you and you've been relieved of your duties. In reality, wouldn't you start to doubt yourself? Ramsey was willing to take back the boat using force, and for what? To launch nuclear bombs!! Wow, dude was confident he was right.

Now put yourself in Commander Ron Hunter's shoes. You are so confident in yourself that you just relieved your Captain of his duties. You got some balls! Well, the Captain takes back the ship. Ron Hunter doesn't have second thoughts either, he takes over the ship again using force!

I think both men had the best interest of their country at heart. But it's hard for me to believe this could happen in reality. In this scenario, I would have to imagine someone would have had second thoughts and just give way to the other.

BTW, did Gandolfini's character just want to go to war for the heck of it? When the ship celebrated that all missiles were terminated. People were either joyful or relieved. Gandolfini was disappointed. I couldn't tell if he was disappointed that there will be no war, or if that was just a look of pain he felt for his Captain.