The truth is that programming isn't a passion or a talent, says Edge, it is just a bunch of skills that can be learned.
Yes and no. I'd argue it depends on how you define "programming". If you're talking about "can code up basic solutions to relatively straightforward problems" then yes, with enough time, most people can probably learn to do that. Considerably fewer ever reach the point where the code they produce is (usually) elegant. Where they're capable of troubleshooting the most elusive bugs. Where they fairly quickly identify solutions that are orders of magnitude more efficient than the naive approach to a given problem.
I tend to think the folks who reach that level are able to do so by a combination of experience and some inherent traits that you can't just pick up in a programming class. An example from my current job:
My employer makes apps. Our app downloads some images over the network when it launches. It caches them so unless something changes there's not much going over the wire, but the initial download can take a while. Up to 30 seconds where the user is stuck watching a progress indicator on the splash screen. At least two different developers had worked on this app. Then the company hired a new guy (not me). One of the first things he did was refactor the image download code to use multiple threads and transfer the images concurrently instead of in serial. With 8 threads the speedup was approximately 5x. His key insight was that most of the images were very small, so much of the total time was latency and not lack of bandwidth. Especially since latency is so high on mobile networks.
Now the previous developers were not right out of school. They had years of experience. They could "program". But they didn't recognize an enhancement with significant implications for users when it was right there in front of their faces. It's possible that if they had been specifically instructed to optimize the image loading logic they would have come up with a similar solution. Maybe, maybe not. But why did the third guy immediately recognize the problem (and put in place a very effective solution) without being prompted? Was that a "skill" he learned in a programming class?
On multiple occasions this same guy has identified long-standing bugs in our app that I'm almost positive no other member of our team would have ever been able to figure out even with infinite time.