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.