I tested it and I got less crazy results with an equally small number of trials (
28 turns, sacred fire missed in 2 and burned 9 times in 25 possible turns it could have).
The misses pretty clearly aren't statistically significant. Using the little stats knowledge I have left, afaik, the probability of getting 9 burns or less in 25 turns is about 11.5% in total (sum of 25 choose x from 0 to 9, all divided by 2^25). I don't think this is statistically significant either, but if anybody wants to tell me otherwise I'd be willing to listen.
In the case of burn chance, 100 trials is probably more than enough (50% is the biggest percentage of an event you can have). In the case of accuracy, the more, the better. 5% is a tiny fraction; 300 would probably be enough if you
really want to.
In any case, I don't think Sacred Fire is broken; I think you two are either just unlucky (believe me, in every generation, people are willing to believe that sim hax is incorrectly implemented) or are counting turns it couldn't burn (KOes, attacks on statused pokemon, etc.).