This is routinely validated on siblings. If the polygenic scores are as accurate in predicting differences between siblings (who, presumably, share substantially same environment) as they are between unrelated people, it means that they detect real, biological things, instead of just some kind of population stratification. The linked abstract, of course, mentions this, and you'd have known this if you had read the article.
Also, your assumption that socioeconomic factors are independent of genomes (that they are just "chance correlates) is also substantially wrong. Genes correlate with socioeconomic factors, because they often cause socioeconomic factors. People are not born into socioeconomic conditions randomly, they are born into socioeconomic conditions of people who share half of their genome with them.
Do you think no biological basis exists? Either way, they are still correlates, even if some aren't causative.
These models are still predictive when tested against control groups outside the training population.
Understanding whether the model is capturing biology is critical when thinking about applying it to IVF. If the model is primarily capturing socioeconomic correlates, those factors will (in most cases) be fixed for all embryos from a given pair of parents. The PRS needs to be weighting _biological_ risk conditioned on a fixed environment if its to be used ethically in this context.
In what case are you expecting the purchasers to be harmed? It seems reasonable to screen for the other factors as well if a correlation exists.
An example of Nature would be comparing well fed children of basket ball players vs children of horse jockeys.
Particulary the legend for figure 5:
> Activated SNPs are distributed roughly uniformly throughout the genome.
If the authors were actually identifying a genetic component to a heritable trait, I'd expect them to observe some linkage disequilibrium. And without any analysis of the SNPs (are they coding/noncoding? which genes are they associated with?) it's hard to believe that they're uncovering actual biology and not just chance correlates with external/socioeconomic factors.
I also find it difficult to trust studies when the lead author fails to disclose a conflict of interest. [2]
[1] https://academic.oup.com/genetics/article/210/2/477/5931053
[2] https://academic.oup.com/genetics/article/214/1/231/5930514