"Writing code is probably something LLMs have excelled at the most. But how much of their ability to write code is due to their understanding of it vs. just them recalling code snippets which were present in their training dataset or their context window?"

This makes me think mostly about how humans work.

Programming is to humans like speaking a language. You have ideas for what to achieve and express, and if you are a proficient programmer then outputting those thoughts in a programming language is second nature.

Programming (like most things humans learn) takes practice. It is NOT enough to simply read a specification and then you know how to code (except for transferring skills between similar languages). You repeat, make mistakes, and learn from them.

I would be tempted to say that humans definitely "repeat snippets from their training dataset". We mainly recall and express from our training/experiences. Creativity is mostly recombination of things already seen.