Sophia, our 11yo, is bright, funny, smart, and constantly tests in the 80s-90s on her Iowa test scores (I keep an Excel spreadsheet showing her progress throughout the years). I would hazard a guess that her IQ is in the mid-120s (her mothers and mine tested around 130), so the nature part was, fortunately, set in her favor.
On the other hand, her mother (especially!) and I are extremely involved in Sophia’s academic life - if you search through my threads here you’ll find a number that deal with education issues - to the point where “education” is more of a facet of our existence than something you do 5 days a week, 6-8 hours a day. For example, during the summer we send her to various 1-week educational camps throughout San Antonio - geology camp, archaeology camp, photography camp, math camp, even Harry Potter and Doctor Who camps. During the school year, not only do we keep on top of her homework (sorry, Hari! 
), she and I will spend an hour every Sunday previewing the upcoming weeks work (especially math, where this has made a BIG difference in her comprehension and confidence.) She doesn’t read just the minimum (1-2 books) on her summer reading list, she reads as many of them as we can fit in, etc.
I don’t want to say she’s intellectually lazy, but perhaps not as driven to find out things as I was at her age. She would much rather watch TV and complains when we ask her to read (I probably did the same, if my Dad would have ever asked me to read), the usual stuff.
So, with Sophia it’s obviously both (nature and nurture). She has the tools, but she doesn’t have the inherent personality traits that make for a self-made “intelligent” person. But fortunately she has parents who care and we’re helping her develop the habits so that when she’s grown she will accept continuing education as “normal.”