It is true that the Holy Fire did not come to the armenians, but "took another way" and came to the true orthodox from a pillar. If it just appears for the "Genuin Orthodox" of GOC that visits this miracle, why doesnt it come just to them. An explanation that it appears to show the world when the true date for pascha is, is also strange, becuase then it could have come to monophysites who celebrate pascha at the same time. I believe it comes becuase there is GRACE in the Patriarch of Jerusalem. This is, I believe, the best explanation.