That is some great analytical thinking! That is one of the skills necessary to be a lawyer. The book is exactly right, actually. The policy (reasoning) behind that general rule is that a citizen shouldn't have to pay twice or be tried twice for a single crime by the government (at least in the U.S., for the same charge). This is a basic due process constitutional right. It is logical, since: 1. if we are innocent, we should only have to be burdened with one trial, and the government better do it right or not at all; this helps us be free to live our lives without frivolous charges. 2. if we are guilty, we should be punished for every crime, not just the first murder. So every murder will be punished, but the same murder will not be punished twice. That's what the book is saying, I think, because this is basic criminal law in the U.S.
Example 1: a guy is found guilty of murder. He serves time. Later, he kills someone else (since he can't kill the same person again, this new person is definitely a new victim!) That is considered a new crime and can be tried and punished again. Otherwise he'd be off on a murder spree without punishment, like you mentioned.
Example 2: A guy is found not guilty for a murder, he will never have to be tried again for that particular murder. However, if a second person is murdered and that same guy is suspected to be the murderer of this new, different person, he'll have to go through yet another trial.
By the way, it goes by crime, not by person. Murder isn't a good illustration, but robbery is. If I rob you, I will get my "due process" (guilty and punished or not guilty and set free) only once. But if I rob you again and again, I will be tried every time, even if I rob the same thing from the same house over and over!
I hope this helps.