Exactly. One of my pet peeves is the misconception that a life expectancy of 35 means a normal adult somehow drops dead at that age. (And leads to arguments like "Oh, don't eat a paleo diet, cavemen only lived to 35").
Socrates lived to 71 in ancient Greece. Yet you know him for being a philosopher, not for living 2.5x the average age (like living to 200 today -- you'd think that'd make a fuss).