Potential monkey wrench: you’re assuming the AI agents we have access to are the same ones crawling and indexing the web for those models. They not only incorporate the text they find while crawling, into their models, but they have access to some kind of web search behind the scenes as well — when you ask a chatbot for information on a product or person or whatever, it doesn’t “go out and look for it” it hits up a web index (which literally could be Google, but is probably something a little different) and then searches the sites the indexer returned.
Your test replicates what happens if someone asks for something specifically on a given site, but not necessarily what happens when you ask the chatbot for info by name/title instead of specific URL. The former is generally much more important than the later.
Just my take - I could be wrong.