I'm afraid I have to go with the non-PC option of 'idiots by nature'. But that's because I know my cousins, Richard and Robert.
They're both sons of wealthy parents - different parents. Both of their parents are high achievers. They went to very good schools and had many opportunities. But from their earliest days it was clear that they were both idiots. Even though I was struggling to get through a schooling system that didn't operate in my native language but rather, in one I barely spoke at the time, I was pwning them in every subject by the time we were in our early teens. They remind me of Barmy Fungee-Phipps and Chuffy Chuffnall from Jeeves and Wooster.
Meanwhile, I who as aforementioned, was being schooled in a language enigmatic to me at the time (though as you can see I got the hang of it), and also living in a tumble-down hovel with neglectful and abusive parents, having zero encouragement or support regarding my education... well, I got a PhD.
[/own trumpet]
So I think idiocy and genius are both in a person's nature. Admittedly, environment can help an idiot to learn to seem less idiotic, and a genius can learn to dumb himself down if he lives in an environment that's hostile to intelligence/education (as I've seen many people do). But in the end, you can send Princess Di to Sevenoaks but if she ain't got the brains she's still gonna fail her O-Levels.