Does "such claims (backed up by extensive evidence)" refer to "claims of miraculous healing"?

Context:
More difficult to evaluate are the claims of miraculous heal-
ing from medical problems. As a physician, I have occasionally
seen circumstances where individuals recovered from illnesses
that appeared not to be reversible. Yet I am loath to ascribe
those events to miraculous intervention, given our incomplete
understanding of illness and how it affects the human body. All
too often, when claims of miraculous healing have been care-
fully investigated by objective observers, those claims have
fallen short. Despite those misgivings, and an insistence that
such claims be backed up by extensive evidence, I would not be
stunned to hear that such genuine miraculous healings do
occur on extremely rare occasions. My "prior" is low, but it is
not zero.