Anyone who specializes in childhood psychology and development will tell you that you are obviously wrong and could provide lots of citations (not my background though). This is hardly a settled topic except it is nowhere near 100% either direction. We have been working with childhood development doctorate level specialists for analysis of one of our children and it is very obvious that the nurture aspect is huge in long term growth.
This research comes from behavioral genetics, not childhood psychology, which I don't know much about. I wonder if the fields disagree.
Point of clarification, Cronqvist & Stiegel (the authors of the conference paper you posted) are not geneticists. They are business professors. Absolutely nothing wrong with being a business professor, but it is a very different field of study.
Twin studies are very hard to mess up in terms of estimating the genetic contribution, but estimating the effect of parenting is a lot harder if you are just using the same data type. To get at the relative effects of parenting vs genetics with any degree of confidence in behavioral genetics, what is really needed is a combination of a twins study and an
adoption study.
Even with the underpowered/mispowered study, the authors find major contributions to savings rates from parenting in people's 20s and 30s. As someone in my 30s myself, I can vouch for how much savings decisions in my 20s and 30s have set me up for a very different and lower stress lifestyle than if I'd adopted a different savings strategy. So I'm afraid even using this study's estimate's parents aren't off the hook when it comes to teaching their children how to secure better and less stressful lives in adulthood.
Now, as you say, the apparent effect of parenting on savings rates drops in peoples 40s and isn't really detectable in twins 50+, but keep in mind:
1) that the authors are controlling for the correlation between savings rate and many other factors which also are influenced by parenting/childhood (e.g. divorce, entrepreneurship, risk tolerance, income, number of children),
2) a lot of effects are they are trying to control for in the linear model likely have non-linear impacts on savings rates (disposable household income is a good example of a variable with a non-linear impact on savings rates) or interaction effects (how the death of a spouse effects savings rate likely varies between people with and without children).
3) that as people live their lives, they have all sorts of life experiences which will influence both their desired lifestyle and savings rate, but which won't show up in the variable table to be controlled by linear models. So the error term is naturally going to increase over time, and every other effect decline, which is what we see with the parental contribution estimates Cronqvist & Stiegel make.
TL;DR This study is using a hammer to hammer in nails when it comes to estimating genetic effects on savings rates. But it's using a hammer to tighten screws when it comes to estimating the impact of parenting choices and environment on savings rates.