Could you clarify "I feel like intelligence being genetically linked is obviously the case everywhere except when it comes to race"?
By "race" I assume you mean primarily skin color, and secondarily some facial features or hair types, yes?
There are a huge number of phenotypes besides skin color: hair color, eye color, blood types, cleft chin, cheek dimples, Hitchhiker's thumb, tongue rolling, Morton's toe, and many more.
It seems like most of them are not genetically linked to intelligence, so I don't know what you mean by "linked ... everywhere".
Could you also clarify what you mean by "race"? Most definitions are not really connected to genetics, which is why it usually doesn't make sense that there should be a genetic link. Eg, the archaic "one drop rule" race definition in the US clearly doesn't make genetic sense - see also the so-called "Pocahontas Clause" https://en.wikipedia.org/wiki/Racial_Integrity_Act_of_1924#T... to show how politics affects that type of racial definition.
(Some people also distinguish between, say, the Irish, Anglo-Saxon, and German races, but then use "black" for anyone with black skin, which seems really absurd since the genetic diversity in Sub-Saharan Africa is higher than in Europe; https://en.wikipedia.org/wiki/Human_genetic_clustering .)
You write "The only way to prove its environment is to disprove the genetic component". There is clearly a genetic component, because there are genetic diseases which result in low intelligence.
We don't need to show that there is no genetic component. We need only show that the the non-environmental effect is low enough that it does not make a useful predictor when correlated with race. Do you think that is impossible?