I'm willing to bet that Jared Diamond understands statistics. He just understands that most of the people reading his article don't. The inaccuracy doesn't affect the article so it's better to be more clear than completely inaccurate.
The thing is, it's not even an inaccuracy. He's entirely correct (statistically speaking). He's describing the concept of Expected Value* without explicitly using the term.
The only thing he could be said to "wrong" about is the idea that a person can die more than once, but everybody understands that that's not actually true. It certainly doesn't "ruin the article" like this poor fellow seems to think.
The other key thing is that the risk he mentioned was not specifically of dying, but of either death or being crippled. Both of those are very frightening prospects, and he simplifies it as "dying five times" when he does the calculation.
Expected value gives you the "If I look at 5000 shower-takings with a 1/1000 probability of a shower-taking resulting in death, I expect to see 5 deaths on average". Of course when applying it to a single lifetime, the correct thing to consider is "If I take showers until I have taken 5000 showers or died, what is the expected number of shower-deaths I will incur", which is .9972.
