That's plainly false. There is no such thing as "purely genetic". If you control for environmental factors that influence the expression of genes correlated with intelligence though, such as nutrition in childhood and exposure to certain chemicals, then the factors that determine intelligence are mostly genetic. This is just obvious. It's practically tautological to say, "all else being equal between two people, their only differences must be genetic".

Where there's some uncertainty is what environmental factors actually influence intelligence and to what extent they matter. Some people think school improves intelligence, but this isn't borne out by robust evidence; meaning, the genetic influence is much, much larger and school's effect is hard to measure.

Here's a thought experiment: if you redirected all the funding for public education to eliminating childhood poverty and food insecurity, would the resulting adults be more or less intelligent? The answer is not at all obvious. Certainly it makes for more "educated" adults by some metrics, but more intelligent adults can presumably educate themselves much better, which seriously undercuts the alleged value of schooling.