I agree with you that "Anyone can learn to code!" is wrong. Anyone
can learn to code...
badly, so badly that they're a danger to every piece of code they touch.
However, dragging software into it is a bit misguided. The value a programmer provides is a service (the production of software) not a commodity (the software). The software has almost no monetary value because it can be reproduced at will. Various DRM schemes attempt to make software a commodity but this viewpoint in general holds humanity back.
More to the point, viewing the production of software as a service rather than viewing software as a commodity demonstrates why programmers are the real value. If you view the C-level execs as retailers of a commodity, their business model makes sort of sense. But if you view software engineers as providing a service, it becomes strikingly obvious that the executives are extraneous, unnecessary middlemen attaching themselves parasitically to a service transaction.