It absolutely DOES hold water - you are perfectly aware of the many, many game scenarios, including official ones, where the PC(s) are clearly described as being the only ones available or in a position to save the world, and where (in official adventures) it is clearly stated that if the PCs fail, the world does indeed end. The Paladin believed he was in such a situation, that his own survival was absolutely necessary to prevent the world's end, and therefore he COULD NOT simply think about one person's well-being or his personal honor, because he had an obligation to the other people of the world not to let them all die. In a scenario where the PC was not urgently needed elsewhere, and he could afford the luxury of dying in the name of his code (or simply because he cared about the man he was trying to protect), sure, the Paladin is free to risk sacrificing his own life in a useless gesture to try to save the man. But here the Paladin has MUCH greater obligations to MANY more people, and will STILL LOSE THE MAN if he fails to save the world (which he obviously cannot try to do if he is dead from trying to fight a dragon.)
If you are an expert at defusing nuclear bombs, and you are on a very tight time limit to prevent a bomb from going off and at the same time a child's life is in danger from some other source, you may feel sick in your heart about it but you focus on the bomb, not the kid because if the bomb blows the kid dies anyway. Sometimes there is no scenario where everybody lives, and in that case you have to save the most people you can. That's doesn't make you evil or heartless. Good people - real or fictional - forced to make such decisions should be pitied and treated with compassion, not berated for failing to do the impossible.
This assumes that one PC and only one PC is the all important character and if this PC dies its all over. What about the other 3+ PC's? The lose of one PC doesnt end.