But that is clearly not the case. Look at the data for life expectancy by age for the US from 1850-2011. [infoplease.com] Yes, life expectancy at birth was nearly half what it is now but the gap narrows considerably if you survived past 20. That is to say, most of the increase in life expectancy at birth comes from curing the childhood illnesses from which many died very young. And while far fewer people lived to 90-100 than now, living into the 70s-80s was not exactly uncommon.
What makes you think that the same trend applied to hunter-gatherers? The lifestyle of those born in 1850 likely has no resemblance to the lifestyle of hunter-gatherers.
Next question -- ever consider that maybe the roughly 50% of people who died around or before age 20 may be a population that's much more vulnerable to "chronic diseases of civilization"? Maybe the reason there weren't many type-2 diabetics or sufferers of congestive heart failure in their 50s is because the people most prone to such diseases were long since in their graves.