How much experience do you have with LLMs exactly? It would be consistent with my experience if Claude stuck in a line of python that just emits a JSON literal with no justification, potentially buried in a large program where an untrained person might not notice it. I don't even trust them if the output consists of structured data paired with source images from the PDF, because I've experienced LLMs fabricating the source rectangles to match the output. I only use tools like this by asking for programs, because as you note LLMs are good at that, and the verification process consists of tool calls to legitimate PDF manipulation tools so I have some confidence everything is above board. Even then I only do this for hobbies, not anything that matters.
Lawyer here. I used to trust Claude as hallucinations are near non-existent now. However for large volume tasks such as due diligence exercises, they still happen. We also tried Legora's tabular review, there were also numerous halucinated provisions in our due diligence exercise.