It's a good plan in theory, but I think it comes off as stupid because she based it off book knowledge. The author has already shown that books and rumors in this society are unreliable, since the books about the north are filled with lies, but then the fl bets the lives of her people on a book claiming the golems are dumb. If she'd witnessed the golems being stupid, or it was at least common knowledge, then the plan would seem more clever than reckless.
Basically, don't base your plan on rumor when one of the themes of the webtoon is 'don't unconditionally believe in rumors'.