It's intelligence even considered to be something that is directly heritable these days? I thought that too many genes and possible gene combinations were involved.
You can compare it to the heritability of height. Two moderately-tall people can have short children, medium-height children, or tall children, just as two tall people can have a very short child, for example. But on the average, the female offspring will be the mid-parental height (average) minus two inches, and the male offspring will be plus two inches. It has historically been observed that the first generation after immigration to the first world is taller than the parental generation, and that the generation after that is still taller, but that after a few generations, the height of the population stabilizes. Height and intelligence are both continuous traits, with strong effects from genetics, but also effects from environment that you can conceptualize as nutritive.
And yes, I would agree that the measurement tool is a factor. I would add, as a corollary, that the traits valued by a particular community might be involved in the definition and measurement of intelligence.
