I disagree, and I disagree because I used to think this way (having lived and breathed programming since age five), until I started to meet people who had started to program in university (which I considered _way_ too late) and who had become excellent programmers. Not adequate-for-a-job programmers, but best-of-breed programmers.
In fact, often better programmers than "naturals" because along the way they had learned a lot of discipline that isn't necessary when programming is fun -- but as every "born programmer" turned professional finds out, programming isn't always fun.