I find it hard to understand why we think it is possible to assume that the influence of genes and influence of environment are independent in this manner.

Given that we know that the environment affects how genes are expressed; and given that it's the genes that happen to be expressed which have more of an impact on intelligence than the genes one happens to 'have', then surely all research in this area which fails to account for interaction between (various) environmental impacts and genetics is bound to be futile?