Even if they do have this knowledge, and even if they could just as easily find it through Google or some other publicly available mechanism, they are most likely just seeing if you'll incriminate yourself. Why do they ask me what I'm doing when entering a country or where I'm staying when I've already given this information to the airline before boarding the plane?

There's a whole line of reasoning behind their questioning tactics that extends beyond getting to the facts. That's why the best legal advice is simply to not say anything, because they are not in any way shape or form on "a quest for the truth".