I've written a lot in the past about hostile corroboration of the claims made by the earliest Christians, including their miracle accounts. Craig Keener's Miracles (Grand Rapids, Michigan: Baker Academic, 2011) provides many modern examples.
Keener cites corroboration of healing accounts in non-Christian mainstream media sources (428, 433, 460). One journalist was an agnostic and intended to write a book against faith healing, but converted to Christianity in the process of doing her research (476).
Regarding a doctor involved with another case:
"Her main physician, Dr. Ronald Kleinman, associate professor of pediatrics at Harvard Medical School, was Jewish. He considered her cure 'miraculous,' reporting the cure both to the Vatican and in a 1997 interview with CBS Evening News." (479)
Another healing converted an agnostic doctor (527). Keener tells the story of a woman who had suffered from liver cancer and apparently was resuscitated shortly after dying. She was free of cancer afterward, and a non-Christian doctor she had gone to when she had the cancer converted after finding out about the healing (569-570).
"One scholar skeptical of supernatural approaches readily grants that the healings occur. He affirms that 'some utterly extraordinary cures' have occurred there, noting that enemies of the Catholic Church and leading medical scientists like Alexis Carrel have been persuaded by the data. He concedes that some cases cannot even be explained psychosomatically; among examples, he lists 'the instant healing of a terribly disfigured face, and the instantaneous healing of a club foot on a two and one half year old child,' shown by non-Catholics to be permanent. Further, he cites a news article about a three-year-old with terminal cancer and the bones being eaten away; after the healing, even 'the bones in her skull grew back. Her doctor, a Protestant, said that 'miracle' would not be too strong a word to use.'" (685)
"Patrick McNamara, director of the Evolutionary Neurobehavior Laboratory at Boston University School of Medicine, and Reka Szent-Imrey, research associate at the Institute for the Biocultural Study of Religion, challenge the traditional intellectual goal of merely debunking miracle claims rather than learning from them. In this 'scenario the hero-scientist' informs the recovering person that no real cure is occurring, 'that instead he is gullible, stupid,' and should appreciate the heroic scientist for informing the patient of this truth. By contrast, these authors contend, extraordinary healings do occur, especially in religious contexts. While agnostic about supernatural causation, they insist that scholars should study and learn from these cures." (609)
Keener recounts the experience of one anthropologist:
"More astonishingly, in the Journal of Anthropological Research one anthropologist reported that during a shamanic funerary ritual in northwestern Ghana, he witnessed a corpse that had been dead for a few days dance and play drums for at least several minutes. 'I saw the corpse jolt and occasionally pulsate' in reaction to the shaman's movements; streams of light invaded the room, and 'the corpse, shaken by spasms, then rose to its feet, spinning and dancing in a frenzy….The corpse [of a drummer] picked up the drumsticks and began to play.' Soon it was again a motionless corpse, propped against the wall….Describing his experience thirteen or fourteen years later, he both continued to insist that it was a real experience shared with the other witnesses and tried to offer an impersonal, materialistic explanation for it, namely, a sort of group hallucination caused by the rhythmic drumming and his exhaustion. In view of scientific research about hallucinations, this explanation seems probably inadequate for an experience that various persons present shared. Still, something like this explanation is not impossible, given the intense ritual context. Whatever the explanation, it differs in any case from conventional Western categories of what should be able to happen." (540-541)
Elsewhere, Keener comments that "Some anthropologists have noted the transformation of a number of other anthropologists' beliefs through their anomalous experiences." (830) Concerning a study of anthropologists who experienced paranormal phenomena: