You’re right about the trees but wrong (hear me out) about the forest.
Yes, programming isn’t always deterministic, not just due to the leftpad API endpoint being down, but by design - you can’t deterministically tell which button the user is going to click. So far so good.
But, you program for the things that you expect to happen, and handle the rest as errors. If you look at the branching topology of well-written code, the majority of paths lead to an error. Most strings are not valid json, but are handled perfectly well as errors. The paths you didn’t predict can cause bugs, and those bugs can be fixed.
Within this system, you have effective local determinism. In practice, this gives you the following guarantee: if the program executed correctly until point X, the local state is known. This state is used to build on top of that, and continue the chain of bounded determinism, which is so incredibly reliable on modern CPUs that you can run massive financial transactions and be sure it works. Or, run a weapons system or a flight control system.
So when people point out that LLMs are non-deterministic (or technically unstable, to avoid bike-shedding), they mean that it’s a fundamentally different type of component in an engineering system. It’s not like retrying an HTTP request, because when things go wrong it doesn’t produce “errors”, it produces garbage that looks like gold.