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.
In the “born programmer” theory, surely the trait begins latent and could manifest at any age depending on exposure / triggers / mentors etc? And university seems a likely time for that to happen; not everybody had access or was given that first nudge into computers earlier in life.
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.