Except that raw unadjusted IQ scores for even the "hardest" and supposedly most culturally unbiased test (Raven's Progressive Matrices) have consistently shown a secular gain of about one standard deviation over 30-to-40 years, due to the so-called Flynn Effect; with much of it concentrated at the low end. The whole notion that these tests simply measure some kind of purely "innate" ability is highly implausible to say the least; even more so when you compare across different cultural subgroups and even totally different countries.

Not to mention that any test of “innate” ability should not be affected by training or practice, but all known tests of supposed innate ability are. Even Binet (yes, the guy who intended the IQ test) found substantial practice effects; these effects were replicated by Gibson (1969).

It's obviously both genetic and environmental. You can limit people with a detrimental environment (extreme example - inflicting brain damage) but cant improve them beyond their their natural ceiling. And yes, tests don't purely measure that innate ceiling.