Imagine a less convenient example, e.g. a binary star system where the two stars are of roughly equal or similar mass (and the two stars aren't [somehow] 'right next to each other'). We'd say or write that the two are orbiting each other and that the center of their orbits is outside both.

If Jupiter was more massive then that would also be the case, i.e. the center of its orbit would be obviously outside the sun. Unless you're next going to argue that the entire universe is arguably 'inside the sun' because " it just becomes gradually less dense the further out you go".