Yes, it is after some processing. I think I'm beginning to see the conditions under which it happens. A good example of the kind of field where it occurs is the Pleiades region, where with a camera relatively insensitive to blue, you have to expose for very long durations to pick up the reflection nebulae, and the stars burn in quite strongly.
I did a HDR composition and notice that after processing, it too shows subtle amounts of this coring effect. I think it is related to the fact that PI never touches saturation levels in its processing - a sort of DSP-like saturating arithmetic. Seems a reasonable choice, but the result is that some very near saturation levels get affected by things like background uniformizing, while the perimeter of the star with hard saturation never gets affected.
FWIW, in the case of the Pleiades, the HDR results look only very slightly better than normal image integration. All the dynamic range is eaten up by those bright stars, and they are among the less important aspects of the image.
I just checked the deBayered calibrated images, and they show some signs of the coring about to happen. It seems that with saturating arithmetic, it will be nearly impossible to avoid this situation, as it happens in the initial image calibration, and then grows worse with additional processing.