I think there is a common thread to the two things. The average JW thinks they know something that others don't, that they know more than the "experts", those more well educated than they are. It's a conceit, one encouraged by the Watchtower, it flatters their egos to think they are better than others, people they resent for having an education. The Watchtower slams traditional religions, implying that the clergy knowingly deceive people, but they have the "magic cure" in their belief system.
It's the same with those who who don't believe in traditional medicine. It's a common misconception by many, not just JWs, that the drug companies and doctors conspire somehow to deprive people of better cures, that they are invested in people being sick. Of course this is propagated by those with a "miracle cure" of some sort. It's nonsense, but works because it plays into people paranoia and resentment of people with a better education.
That is not to say that all alternative medicine is bunk. I have used meditation, acupuncture and massage therapy, but those are fairly mainstream, with some science to indicate they are effective. You just have to be careful, there is a lot of questionable therapies and the internet is full of misinformation. Most of these cures are being pushed by someone who has a financial stake in it, so that is a red flag.