On the other hand, there's been quite a bit of theorizing about why people have the capacity to live so long beyond child-having and child-raising age in the first place. It can easily be construed that there's some advantage to the group (the natural human social unit is not a nuclear family but more like a small tribe or whatever) having some members around who are not themselves producing children but are still capable of helping out -- and also some who are old enough to have learned a lot of stuff and remember things that only happen rarely (as in "we had this kind of freak weather once when I was young and this is how we survived...") Of course you don't need everyone to live to age 70 or beyond with a clear mind for this, just a few.
Assuming, of course, that in the depths of prehistory those human tribes could already make each other realise that they had seen such weather/other in the past too

In my view it is very unlikely that such a condenced, conclusive view can be correct in this matter. It is very highly unlikely that humans exist as they do regarding such issues (eg the age you mentioned) in such a direct link to the ability to have offspring. I also suspect that the majority of organisms on the earth do not have that ability anyway (eg virtually all of the types of ants in any colony).