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In their significance declaration Cox et al. state “We show that changes over the past 35,000 y are largely predicted by genetics but also identify specific shifts that are more likely to be environmentally driven.”
In their abstract and more so their conclusions they are far more reserved in their wording and for good reason. Their claimed effect, such as it is, is tiny compared to the internal variation of e.g. their Mesolithic sample. The predictive power of polygenetic scores is very low as they state themselves. But then the skeletal stature too is not normally well known but regressed from individual well-preserved bones. When I looked at the four regressions used and listed in a well accepted text book (Herrmann 1990) and plotted the difference of their outcomes along a range of measurement I found them to differ by five times the largest of their stated error. Just one single, simple assumption is more than enough to explain the whole of their observation: If the very few Paleolithic burial are indeed exceptional, and their grave goods make just that plausible, aren't they to be expected to be of slightly above average build?
To reiterate something I said before: Whenever you calculate a regression on a finite number of random data points, you will get a definite result and the slope will never be zero. In Cox et al. I fail to see anything more than that.
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