I've heard the same said of many of those who've gone through near death experiences. I think God knows our hearts better than we know them ourselves, so the real healings that have taken place have less to do with physical wellness & more to do with people seeing their natural human doubts removed.
They think they've been touched by God, and they believe and become more faithful.
I'd use the phrase "firm believers" where you used the term "faithful" & I think all of us are touched by God.
Even folks who go on pilgrimage there who are NOT healed generally report a renewed faith (not everybody).
I see some healings you don't seem to recognize...
NDE's are key.
There are already four published peer-reviewed, controlled, long-term medical hospital studies of near-death experiences.
All four produced statistically similar results.
The experiences described by the control group in all four studies were very similar as to order and content.
There are other individual cases which are quite striking.
Essentially, the science, read in totality, strongly indicates the existence of a detachable consciousness which continues for at least some time after clinical and even brain death in about 20% of people (the rest report no memories, which might mean they had no such experiences, or it might mean that they did and don't remember them or don't want to talk about them).
And then there are those people who were not clinically dead but who have had direct encounters with divine beings, angels, spirits, etc.
The world is a strange place, both physical and spiritual. We understand some aspects of the physical world, but the spiritual world we can't even figure out how to test. So, all we have there is anecdotal evidence and (competing) revelations.
And, of course, even with the same tradition (e.g.: Christianity) there are passionate, even violent, differences of opinion over the MEANING of revelation, let alone the authenticity of it (voir this thread, for instance).