There are way more metrics in there, including more crime stats. The one somenameforme chose to highlight has a ton of ambiguity, leaving it open to the reader to guess that maybe all the program participants were arrested merely four times by age 40, so in fact this program sucks (plus somenameforme's scare-quotes on "only"), but the paper itself contains far more information and paints a clear picture of outstanding success for a relatively small intervention. Somenameforme's characterization of the study doesn't match the contents.
If that's the evidence a person's citing, the evidence they've cited is screaming "this works great", not the opposite, as implied. It may still not be true, but if so... cite different evidence to support that, because this study says this intervention was wildly successful.
But read further down on the details and that difference disappeared almost immediately after the end of the intervention. It follows in line with a well known fact that childhood IQ is primarily driven by environmental factors whereas adolescent and especially adult IQ is primarily driven by the IQ of your parents - paradoxically, strengths or deficiencies in earlier life notwithstanding.
And their decision to set the baseline for arrests at 5+ is obviously doing something akin to p-hacking. It makes it clear that near 100% of the entire sample (males at least) ended up in prison, likely multiple times. The ROI from the program had nothing to do with increased productivity - it was driven almost entirely by less time spent in prison. It led to the interesting fact that 93% of the ROI came from males, precisely because the females had a much lower baseline criminality rate.
In a nutshell, the main benefit of the program was reducing the criminality rate of the experimental group to a level that is still orders of magnitude higher than for society at large. That is a good thing, but it also emphasizes that something like this would only be the beginning of special care needed to try to ensure these sort of people could live remotely decent lives.
One clever way this is measured is twin studies, which also are not what most people, particularly those who prefer to write more than read, think. You don't search for twins separated at birth, but instead compare the differences in a trait between identical and non-identical twins. If the variation is greater, then the trait is generally significantly heritable. So for example - height would be an obvious one. By contrast the variation in accent between identical and non-identical twins would be zero.
Direct genetic causality is not the only mechanism through which genes select for phenotypical traits. Genes also select and interact with the environment.
Unlike the individuals you have cited, James Watson is a geneticist, spent his entire life studying and working on genetics, and in fact was even the person who discovered the structure of DNA. But because of his views on the genetic aspects of IQ (which inherently becomes intertwined into race, as race is just shared genetic ancestry), he was completely demonized, his career destroyed, and various honors revoked. Higher profile people speaking on these topics publicly know this all too well, so it mostly just turns into cheap virtue signaling as opposed to adding some genuine insight.
In your case, the examples they've offered are simply wrong, as would be immediately apparent with the most typical method of measuring heritability!
This is a "not even wrong" situation. Is cognitive ability significantly genetically determined? Maybe, maybe not. A broad heritability statistic from a twin study isn't going to resolve the question.
Here's a good link for you:
http://bactra.org/weblog/520.html
I promise, the author has studied and thought more carefully about the question than we have.
Fair warning: you would not be happier if I cited a molecular geneticist on this subject. Your argument gets even harder to sustain once you bring GWAS into the picture.
It'd be akin to arguing to somebody who wants to claim the Moon landing was faked, and after the rather straight forward rebuttal of their argument links to some blog in the tens of thousands of words from some statistician they claim is "very smart." It's silly.