'Extremely rare' does not equal 'miraculous', it equals 'extremely rare'. The difference is philosophical. Rare events will occur naturally by virtue of probability, that does not imply some supernatural intervention breaking natural law has taken place.
It becomes miraculous when it coincides with an answer to prayer. Extremely rare events by their definition will probably not happen when you wish them to, but a prayer certainly helps it to happen when it is needed.
I sometimes attend Mass at my local catholic church and there is always one or two parishioners ill in hospital or dying in a hospice, and at some stage the entire congregation is led in prayer by the priest for these unfortunate individuals. I am not entirely blind to the value in this; keeping loved ones in our thoughts at their time of need strengthens bonds and communities and maybe sometimes the psychological boost of all that well wishing might indeed spur someone on to a speedier recovery.
But on the other hand those awful things, facts and figures, they don't really lend support to any notion of anything truly miraculous going on. Catholics continue to suffer and die in our hospitals at pretty much the same rate as all other groups, despite the intercessionary prayers of hundreds of well wishers. If there were any real effect you can bet that NHS managers would be on to it like a shot, dispensing with expensive hospital consultants and pharmaceuticals and replacing them with much cheaper teams of christians praying.
Well of course, that does not happen, and pretty much every ill parishioner will take the view that why not have the best of both worlds, apply the best insights we have gleaned from research, and then pray as well, what harm could it do ? Maybe the harm is little, maybe the benefits might outweigh whatever misgivings a rationalist mind might have about it. But it does seem to me to involve a community wide tacit indulgence of a curious sort of doublethink. We are modern people, we value research and evidence, but we are still going to witch doctors on the quiet.