They both revolve around their barycenter. So neither one revolving around the other is ground truth. In practice either one can be the right choice (earth at center for video game, sun at center for astronomy predictions).
People are using natural language. And considering the barycenter sits inside the sun or close to it (relatively), it isn't that wrong of a statement.
While you're technically correct, everyone already understood. We could be more technically correct by talking about the galactic barycenter, or even more by talking about the universe as a whole, but the accuracy gains by that added complexity doesn't benefit the conversation
