All "heritability" research is just an analysis of correlations between genes and expressed behaviour. On these grounds a scottish accent is highly heritable, since the accent correlates extremely highly with some genes.
We do not have the means to create new human beings with different genetic profiles and observe them accross many environments, as they develop, to determine if "somehow" a gene causes anything so macroscopic like "intelligence".
So, quite literally: we cannot do science. We cannot create experiments to test hypotheses.
Genes have no plausible mechanism to "cause" intelligence. If they play a significant role, it is a very large number of genes building tissues which are completely opaque (brains, etc.) whose interactions with the environment are completely opaque.
Heritability research, and "psych-genetic research" of this kind is, necessarily, pseudoscience. It's adhearents are the poorest statistians and have the least understanding of the scientific method you could hope for.
We have no scientific theory of intelligence which provides causal variables that we can experiment with; we have no theory of biological mechanism, likewise; we have no theory of genetic mechanism --- all we have are some aging loons with stats software content to put iq-test-scores (ie., people competing patterns of shapes...) and Genes into it.
Whatever can be found by these loons isn't worth a scientist finding. "Data" isnt innocent, it is collected and used for a reason; and pseudoscience isnt innocent.
Correlating genes with ESP ability is likewise nonesense, and that has as much scientific merit.