If results are influenced by education or upbringing then the test does not measure "intelligence" as intrinsic ability.

That's actually probably a very difficuly topic: cam we devise a test that measures intelligence irrespective of education (i.e. training)?

This begs the question. How much of "intelligence" is intrinsic? We don't know. It's not zero (we know there are genetically-mediated cognitive deficits), but it's very plausibly not meaningfully intrinsic in most people.