If that were the case, then you wouldn't get the transfer learning from models being trained on programming languages, to reasoning applied in a non-programming context, which has been universally observed for all these models. They are learning abstract "thought patterns", not just interpolation.

Learning a programming language (or any complex skill) just by reading a book and looking at examples, without actually practicing it yourself, is basically impossible, even for ourselves, let alone an LLM. It is amazing how well the LLMs can do at programming in cases where they were trained on masses of well-commented examples, but without also being able to learn "on the job" themselves, you need to tamper expectations.