I'll jump on the bandwagon of saying there's more to this than meets the eye. The way the GFCI outlets are mass produced as identical devices, I think the odds of one being able to reverse the hot and ground are astronomical. Coupled with the previous observation that the ground goes 'to', rather than 'through' the outlet, the odds are astronomical-squared.
The outlet tester gives a possible interpretation of the pattern of lights, not a definitive answer. With 2 lights lit in the 'hot-ground reversed' pattern, it's indicating voltage between ground-neutral and ground-hot. Another cause of this indication would be 'neutral connected to hot', which I believe would be consistent with your measurements and observations. While I still find it unlikely that the outlet would do this, the odds are IMO somewhat less than astronomical. There are probably other causes of the outlet tester's indication, too.
