You can find evidence for this in numerous ways. For instance studies looking at classical Greeks 'of renown', found a median life expectancy was 70, and average life expectancy was 71.3. [1] Even in the Bible one finds numbers that match up basically exactly, 'Our days may come to seventy years, or eighty, if our strength endures; yet the best of them are but trouble and sorrow, for they quickly pass, and we fly away.' You can also find things like the minimum age for Roman Consuls being 42 years, and so on endlessly.
And all of this was in an era when there were no vaccines, no knowledge of germs or how disease spread, and when cutting edge medical science had to do with balancing the 4 humors (blood, phlegm, yellow bile, and black bile) with some sort of an elemental association of air/water/fire/earth with each. Eating well and exercising can indeed take you extremely far, because it damn sure wasn't their healthcare doing it. That said modern medicine has basically been a miracle worker for childhood survival, but once you make it to adulthood - your body is strong enough, or can be made strong enough, to get you most of the way to your expiration date.