Semantics aren't silly in science, nor in education. I don't think it's so uninteresting as to be worthy of ridicule. It is not, in fact, obvious to the layperson that the Jupiter-Sun System would have a barycenter that doesn't lie inside the mass of the sun. The casual mental model (and all physical models I've ever seen) of the solar system we all share puts a metaphorical or mechanical axis through the center of the sun, around which we all the revolve.

What may be a shorthand for you is the obscuring of deeper truth for others, and discovering that deeper truth is a wonderful 'Aha!' moment for those who experience it.