I spoke to a very devout Greek friend, and he said he had spoken to a monk from Jerusalem who didn't believe in the flame.
The Patriarch (of Jerusalem) found out about this, and told the monk that there is a window looking into the Sepulchre, and just before he (the Patriarch) goes into the Sepulchre, to sit and watch through the window.
The monk did just as he had said, and this is how it went:
The authorities searched & stripped (not entirely) the Patriarch. They went inside the Holy Sepulchre and searched it for any possible light source, and then the Patriarch entered, and the authorities sealed it off.
The Patriarch then bowed his head with his candle in hand, and began praying. At first nothing happened, but after several minutes of sitting in complete silence praying, then the inside of the tomb was lit up by a bright blue light and suddenly the candle of the Patriarch lit spontaneously. The Patriarch remained with his head bowed and eyes closed while the flame of the candle burned underneath and around his face. (though he was not burned, not even his beard) Eventually the blue light had subsided and the Patriarch emerged from the tomb with the Holy Flame.
The monk that witnessed this was dumbfounded and apparently very pale and very shocked. Eventually, he went with the other monks, who saw how pale and shaky he was, and they said, "Ah, so you went to the window too?".
Needless to say, this monk now believes in the Holy Flame.
Again, that is an account from a friend of mine here in Greece. I cannot vouch for the story or it's authenticity, but I certainly do believe in the Holy Light.
If you also think about the known fact that on Theophany when the Patriarch places the cross in the Jordan, it miraculously reverses its flow, then I feel there is no doubt about these other miracles.
I don't think you have to believe in these miracles, but when people actively try to disprove them, then I would say they have questionable faith.
The Apostle Thomas didn't believe Christ was risen, but he still didn't try to prove the others wrong, he simply wanted proof. (though that isn't a model for us, certainly)