After talking to her, it comes down to distrust of the medical industry. The argument I hear is that the number of vaccines administered to children has been rising. The point of the medical industry is not health, it's profit. The process, not the vaccines themselves are the issue because the system could release something dangerous and nonessential and that would be okay as long as money is made.
Once you assume bad faith, all the data and information you could gather is worthless. It could all have been cherry-picked, or statistically manipulated. Belief in bad faith comes from distrust. Merely removing thimerosal from vaccines and doing studies disproving a lack of causality between vaccines and autism does not build trust. Scientists are flustered at the moving target the anti-vax movement presents [1]. Thoroughly disproving a theory just presents more new theories. The problem was never information.
Trust (or lack thereof) is the biggest threat to public health.