So I read about this study, which was to determine how much people who use "alternative" medicine really care about the science. The results are not comforting:

When asked what they would do if a government agency said that the supplement they use most often was ineffective, 71% of regular users reported that they would continue to use it. In the follow-up survey, respondents were asked what they would do if the FDA specifically said that the supplement they use most often was ineffective to see if using the FDA's name vs an unknown government agency would alter the result. The addition of the FDA did not lead to different responses. Once again, two thirds (67%) of regular and sometimes users said that they would continue to take the supplement.