[pjbeam]

There is no checkbox for someone to check that once done that's it, they're now a programmer and can just do it in every situation without learning. I work with very talented and experienced developers who learn new things frequently.

The ability to constantly self-teach is table stakes for programming. I suspect what you're asking is is it possible for someone to teach themself from nothing enough to get a job and I think so--although it depends on the job and there is definitely a progression, or a "meta-career", that goes beyond the basic act of performing fizz-buzz or inverting trees for interviews.

If you aren't asking about employment the answer is still yes--it's quite accessible to self-learn enough programming to do something useful, satisfying, and or fun. Does that mean everyone is capable of rising to any challenge on any day based on what they've already taught themselves? Of course not.

My read of your post, which may be missing something important, is that you've succumbed to the common trap that there's some mystical mountain that once you climb it you're good and the journey is over. This seems to be a common viewpoint of non-technical people.

Sure, with experience and or education the surface area of problems that one can readily solve grows, but no one can solve all programming problems merely with what is already in their head.