Idiocracy mixed being educated with being intelligent. Being educated is not hereditary and does not (I think) affect intelligence of your children*
Satisfactory nutrition and exposure to positive and engaging environments during childhood affect your intelligence no matter who your parents were
* other than that educated parents are more likely to provide the positive and engaging environment, maybe? Not in the least due to the correlation between education and $, which certainky affects both nutrition and the environment (e.g. toys, lessons, travel, etc.)
Late disclaimer: I have no idea if this is what the scientific areas that study human intelligence believe