Wouldn't that same logic exclude evidence from Google searches, like "how to get away with murder"?

Yes? Which makes it feel like the answer is just “No.” Unless you use Mullvad, TailsOS, and don’t log into the service. But I’m not sure if that’s “ethical” for Google/DDG searches and it’s not really possible for Claude/Kagi. I would assume that simply using a “secret” account isn't a magic way to avoid discovery either.