In that link it is due to the wavelength used (extreme UV, which shows only active regions as bright, and the prominence layer surrounding the limb.)

However, in many amateur pictures taken in the H-alpha wavelength (like in TFA), the artistic choices come into play, as you said. In the Simon's first image the prominence layer (just outside the limb) is shown as-is (positive), while the disc interior is shown inverted (a negative; note e.g. how the sunspots became white). This is done to get a somewhat more "3D look". In a normal, non-inverted image, the mottles and filaments show up as dark features on a bright background, while inverting may make them look more "natural" (to some) - sometimes downright "casting shadows" (a solar filament often has a brightening around its base - which becomes dark after inversion).

Source: I'm the ImPPG's author (and enjoy solar astrophotography myself).

Just a side note, the opposide effect is can be achieved with a phenomenon called Subsurface Scattering (also used in 3d-cg). This has nothing to do with stars, though - unless a star exists that is translucent.