My school district provided early exposure via apple II computers. They showed up one summer with an extracurricular summer workshop and then one to two per classroom, and a computer lab in Jr. High. And while there was an Atari computer at home, I basically had all of my meaningful early exposure to programming via the school district, and the teachers who were willing to spend extra time learning about and then sharing how to use them. Starting at probably age 8 or 9, I used basic and then later logo. The logo continuing off and on until 8th grade when I was using functions/procedures, getting user input, redrawing the screen, etc. By 8th grade my programming was beyond the scope of the curriculum or programming knowledge of the teacher. These skills then lay dormant for 4-5 years resurfacing in college with the first two years of CS course work. Which then led to computer support employment and then high end systems/networking employment.
It is impossible to attribute my skills to nature v. nurture, but I believe that any meaningful early exposure to computer languages, problem solving, or independent exploration of programming to solve a problem or provide something new is a worthwhile investment.