Here is a image of the sun reflecting off a gazing globe. Its a 100% crop, but no black ring.
The effect is more pronounced the greater the contrast (steep brightness gradient) and smaller the blown image, i.e. stars and hot pixels are ideal to produce dark halos. The sun in your image is more extended and bright also outside the saturated region, so sharpening shouldn't produce as easily visible halos.
This is a straight conversion from raw to jpg in LR 4, all the settings are nominal, no sharpening or NR.
Isn't sharpening applied when using nominal settings? (I'm not too familiar with LR4, but other software apply it by default) If you push sharpening using unsharp mask I'm sure you can produce a dark halo around the bright dot in the right hemisphere. Just to illustrate the effect. (looking closer at your image there actually seems to be a dark edge to the white spots [not the sun] - implying some sharpening may have actually taken place?)