I'm sorry, but you're completely wrong. As long as the document can fit within their context window, which are up in 255k+ token region now, they can easily generate valid summaries. They do hallucinate at times, and the context can be used to abuse them into hallucinating, but they are far more reliable than you think they are.
Thats how coding agents work. They can parse documentation and headers produced well after their training date, and operate on them successfully.