I always wonder when do they stop considering the outer layers part of the star and not relatively dense solar wind soup. Nobody says Earth has 7000km radius, even tho there's traces of exosphere past 500km.
The radius is based on visual observation. We have good theories and models about what's happening inside the star. We are quite sure that it's mostly empty space inside the radius. But that's not a good enough reason to say that the star's radius is anything other than what we see through our telescope.
The outer boundary is the point where a photon has a ~50% chance of escaping without encountering another particle.