"I drew a woman born in 715 CE in the Yangtze Basin. It claims that 96% of women were married, the average age of marriage was 18, and 44% of women died before age 15. Clearly these facts can't all be true simultaneously." Umm yeah they can be true. Dead people are not counted. The straightforward interpretation is 96% of women living to 18 years or greater marry at some point in life. However the app has bigger problems, namely it does not seem to select from the distribution correctly, pre 1500 lives seem to be vastly over represented.
Yes, if a human told me this collection of facts I would assume they failed to properly explain their methodology. Given that the LLM is just making up numbers (see the "sources" page, where these are listed as "attributed",) there isn't really a methodology to explain in this case.