Environmental factors are inherently much more difficult to study in social science than genetic factors are, because causality does not imply correlation due to robust violations of the faithfulness assumption. Basically, much of the environment that we are interested in studying are environmental interventions that can be applied to improve things, but people are already trying to improve things, which likely leads to all sorts of correlations between the application of the environmental interventions and the problems that exist, so as to cancel out the correlation induced by the causal effect. Intuitively, you can think of this as "going to the hospital correlates with dying, but much of this is because hospitals have the option of preventing death, not just because hospitals cause death" effect.

Behavior genetics works best when everything is linear and interaction effects are negligible. Two major things to watch out for are what I'd call AxC (aka gxe or gene-environment interaction) and AxA (aka epistasis).

AxC refers to the case where if your child is above average in a genetic trait, then they benefit from being raised in by one kind of family, while if they are below average in a genetic trait, then they benefit from being raised by the opposite kind of family. For example if you imagine that there are some treatments that would work well for highly-genetically-intelligent kids but wreck havoc on highly unintelligent kids.

Behavior genetics usually cannot model AxC, instead it assumes all AxC to just be A (genetics), ignoring the C component. This seems relevant to your question, since in a sense by positing an innately intelligent kid, you are holding A constant, and that would make it more appropriate to attribute AxC to C than to A.

Even worse is AxA, which refers to the case when you've got two genetic factors that work well together, as well as well with neither, but work badly when you've gotten one or the other. However, that's a rather elaborate and extreme effect, so it is unclear how much of a thing it is. I suspect it might happen a lot due to chaos, which tends to make everything interact, however that could also make it interact with E, leading to AxE, which behaves differently.

For the record, in the presence of AxA, twin studies will be biased against C; they will count AxA as a negative amount of C, plus an extra positive amount of A. On its own, this effect might be fairly mild, but if C is lowish, then due to the point I mentioned in the other comment, that will lead to dramatic biases.

I should probably also mention AxE. Twin studies just attribute AxE to E, so it's if anything biased against genetics, but not in favor of rearing, so whatever.

Behavior genetics squares the effect sizes, which biases it very strongly against smallish effect sizes (where "smallish" includes effect sizes on the order of magnitude 0.3, which would often be considered "large" for social science because it is rare to get effects that large). It is possible for the variance due to shared environment to be small, even though the effect of shared environment is large. See this twitter thread for more detail:

https://www.twitter.com/tailcalled/status/1522876250381066242