Even then the definition of the surface is different than the definition of the surface of, say, the Earth, so I'm not sure what "outside" the Sun means precisely.
Pedant? Or maybe just making conversation about the interesting differences between human experience and understanding of terms and what definitions astronomers use. Why do so many people on HN react as if every comment is a competition?
The only planet with a barycenter with the sun outside it's radius is Jupiter. And that only slightly. (with an altitude of 0.07 of the sun's radius)
The earth-sun barycenter is 0.0006 times the sun's radius from it's _center_