At the risk of stretching the analogy, the LLM's internal representation is that theory: gradient-descent has tried to "explain" its input corpus (+ RL fine-tuning), which will likely contain relevant source code, documentation, papers, etc. to our problem.

I'd also say that a piece of software is a theory too (quite literally, if we follow Curry-Howard). A piece of software generated by an LLM is a more-specific, more-explicit subset of its internal NN model.

Tests, and other real CLI interactions, allow the model to find out that it's wrong (~empiricism); compared to going round and round in chain-of-thought (~philosophy).

Of course, test failures don't tell us how to make it actually pass; the same way that unexpected experimental/observational results don't tell us what an appropriate explanation/theory should be (see: Dark matter, dark energy, etc.!)