I remember the measles vaccine debate very well.
From the article:
"In fact, a review of the VAERS data reveals that many of the death reports for MMR vaccine involved children with serious preexisting medical conditions or were likely unrelated to vaccination (e.g., accidents). These complete VAERS reports and any accompanying medical records, autopsy reports and death certificates have been reviewed in depth by FDA and CDC physicians and no concerning patterns have emerged that would suggest a causal relationship with the MMR vaccine and death."
At the same time I think it is natural, even expected, for grieving families to look for a place to lay blame. I couldn't imagine losing a child.