It's a difficult one. I'm an engineer, I rely on simulations rather than hard math most of the time. While the extremes may say something about extremes in general, but one important thing to realize is that these extremes live in most probably non-Gausian tail distributions. Naseem Taleb wrote some relatively accessible pop-science stuff on that. There are however very few people, even mathematicians i would trust with drawing strong conclusions from non-Gausian tail distributions, and the epidemiologists for sure aren't among them. All I can say: read Taleb, he wrote some great down to earth stuff about the dangers of making assumptions about tail distributions that should be required reading for everyone who feels it is usefull to look at the properties of tail extremes.

A second issue is 'if' the extremes tell you something, 'what' it is they tell you. Lets say you have a military system in a perpetual war where a hero, someone who risked his life to safe his comrades, gets a promotion. Lets say five promotions lead to a situation where the soldier is promoted to a position where he never has to see the front again. Lets say a coward will never get promoted and always hides away in the face of danger. Now at every battle, the hero has a 10% chance of surviving and getting promoted and a 90% chance of biting the bullet. The coward has 90% chance of surviving the battle without a promotion and a 10% chance to bite the bullet. Now lets say there is one big battle every month. The coward would have a 59% of living through the first five months. The hero, on the other hand would only have a 0.001% chance of making it. Look on a decade further into the war. If we started out with a milion cowards and a milion heroes, after their 10 years tour of duty we will be left with 10 heroes and 3 cowards. This means that eventhough almost all heroes died in the first five months of their tour of duty, eventhough the life expectancy of a hero is significantly shorter than that of a coward, the hero still has the best chance at finishing his 10 year tour of duty.

Hopes it makes sense like this.