I think the OP is conflating two things, namely that some people don't trust the scientific method and some people don't trust the way science is conducted. The distinction may not be explicit in how the deniers go about things, but I think it's good to understand the difference because while there really isn't a good reason to distrust the scientific method, there can be really good reasons to distrust the current structural state of scientific research.
With the anti-vaccine folk, I don't think that the problem is that people don't trust science- a lot of anti-vaccine folk refer to published research in their criticisms- though the published research is frequently dubious. I don't think they trust scientists in general and I don't think they trust that the scientific process is carried out with integrity. Neither these things are irrational at all. The notion of the noble scientist in the lab coat, slowly and steadily chipping away at human ignorance is naive at best, though it might be appropriate for something like particle physics, where there isn't a lot of profit at stake.
Right now, most (so I've been told) agriculture research is funded by Monsanto and Cargill and most pharmaceutical research is funded by members of PhRMA. Also, history has demonstrated repeatedly that there will always be scientists who are willing to exchange their integrity for money. A healthy distrust of science is, well, healthy. Scientists are people, and people fuck up, even large groups of people. The peer review process isn't perfect. This distrust taken a step or two beyond healthy results in a complete distrust of the entire medical science establishment. Though I would argue that this type of knee-jerk distrust is no less healthy than blindly trusting the medical science establishment.
One way to dispel the fears of biased research would be to let the information flow freely, but that isn't how things occur. Have you ever tried to conduct a literature search on vaccine research without a medical research database subscription? What you find out is that if you actually want to read a lot of this research, you either have to subscribe to a peer reviewed journal or you have to drop $15-45 to purchase the right to download an article.
But even free access to information wouldn't be enough, because when you do get your hands on some published research, you become aware that there are generally some pretty opaque statistical techniques used to make sense of the data and that even if you understood the significance of those statistical tests, you probably couldn't get your hands on the data to verify the results yourself.
Maybe that type of evaluation seems like overkill, but it is actually how one would weigh the evidence on a given subject because there are instances where a reevaluation of presented data can result in significantly different conclusions than those presented by the study's author. You can spend a lot of time and money doing it, but unless you are doing so with every bit of research you happen to accept as valid, you are also likely swallowing misinformation.
I think that it is perfectly rational for a person who lacks the time, money and expertise, someone how is also aware of the tenuous balance between integrity and money, to be skeptical of scientific results as presented by the scientific community and disseminated by the scientific press. An analogous process occurs when people show a complete lack of skepticism and accept as the words of Einstein all scientific results as presented (a process which occurs quite frequently among the anti-anti-vaccine crowd).
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