Well, I don't agree with it in a literal sense. Let's say you have two groups, one of a million people and one of a single person. They are all going to die, but you can press one of two buttons to save one of the groups. (Kinda a reverse trolley problem.) I'm going to save the million people. So, in that very literal sense, I disagree.
I like a lot of what @parallelluniverse said above. Rather than repeating it all, I'll just say that the statement is definitely more about human nature than the words being accurate.
I would take it one step further: the point of the quote is to be able to utilize the reactions people have as parallelluniverse describes.
Say, for example, Country A and Country B are at war, and I want to convince everyone to support Country A for whatever reason - good or bad. It is not very effective to tell numbers about the damage done and how many people Country B has killed. It would be much better to pick out a single citizen of Country A and tell the story of how Country B ruined their life and raped their daughter and then killed them the day before they could graduate from college. Now, I'm pulling at heart strings, and people are more invested. Even if Country A has actually killed far more people of Country B, I have convinced people Country B are the "bad guys," because they are so affected by the personal story. Unfortunately, this leads to fake stories being concocted, or at minimum exaggeration. The fact of the matter is that both Countries have probably done a ton of bad stuff, because war is messy, but the quote you reference is a lesson in messaging.