I work at a medical school and am married to a high-school science teacher who used to teach experimental design. I believe that most people in this country don't really understand the fundamentals of science and how scientific experiments are designed, carried out and reported, so they "believe" the reports that agree with their desires and disagree with those that don't.
Doctors offer chemotherapy as a treatment because statistically people are more likely to survive longer with it than without it. Yes, it's pretty hard on people, but cancer is, too. It's a question of risk vs. benefit, the same as with any other medical treatment. Anecdotal evidence (stories about individual experiences) is what people used before the impartial scientific method was developed a couple hundred years ago, when most people died young of infectious diseases. It's not proof of anything except a few people's experiences.
The media that actually writes the reports most people see (since most people don't read the articles published in scientific journals) often don't include the nuances in the original, or the fact that scientists often conclude that more research is required. And most people don't understand that articles published in scientific journals 1) have to pass muster in the
Institutional Review Board that each institution doing research must have, and 2) are reviewed by experts in the field, before publication, to ensure that the study design, analysis and results are all done correctly.
Even when drug companies finance studies, these procedures have to be followed, by law and treaty (a result of the Nuremberg trials, after the Nazis did unethical experiements on humans). Paying the cost does not mean dictating the results. Any relationships have to be disclosed and are published in the journals along with the articles.
The National Institutes of Health don't pay for drug studies, but they provide grants for most of the basic scientific research that is done in this country.
According to Centers for Disease Control Director Dr. Thomas Frieden: "This flu vaccine is made as flu vaccine is made each year, by the same companies, in the same production facilities, with the same procedures, with the same safety safeguards" and "[t]hat enables us to have a high degree of confidence in the safety of the vaccine."