There've been a number of studies on this, and they basically find otherwise. About 50% of the variability in intelligence is explained by genetics (nature); 1

There've been a number of studies on this, and they basically find otherwise. About 50% of the variability in intelligence is explained by genetics (nature); 10% is parental investment (nurture), and 40% is peers (which includes education, but also local communities, friend groups, etc.). Genetic heritability actually grows as IQ is measured later in life, reaching up to 80% by late adulthood. This effect could be explained because raw intelligence is usually correlated with several environmental factors that then factor into the "nurture" and "peers" components, eg. more intelligent parents are more likely to be highly educated themselves, better able to provide help with homework, higher income, live in a zip code with other intelligent people, can afford college, can afford tutoring to get the kids into an elite college, etc. The literature is too extensive to provide individual citations, but Google for [genetics of intelligence] or [heritability of intelligence] to get a sampling.