When I solve difficult puzzles, the average time of some is too fast to get three stars. So I checked the time trial history (or rank). Some results are insanely fast. I think those results were obtained by someone already knows the answer.
So, I suggest that when you calculate the average time, you need to include only first trial time except second or later trial times. If you do, when I try second time and the result time is faster than average, I might have three stars but my second score may not be reflected in the average time.
Sorry for my aweful english.