Still needs the environment to be able to access the teaching (like taking them to school every day, not constantly telling the kid 'School's shit and those teachers are idiots', possibly doing reading and spellings, buying resources or making them at home, setting questions or projects where there isn't anything left to do from school, allowing books, giving permission to do additional activities, making sure they're properly fed and clothed, not giving them a thump for thinking they're something special, not training them to never, ever mention how crap it is at home in case somebody intervenes).
Goes on at secondary, too - making sure they have somewhere to study, going on the trips, doing the activities, having the equipment, agreeing for them to stay on at school past 16, paying for UCAS applications, completing the parents' part of the grant forms, not telling them that university's not for kids like them.
Academic success is absolutely dependent upon parental contribution irrespective of natural ability.