Considering that vaccines (in general) have been deemed "unavoidably unsafe" at the Supreme Court level, they are not completely unjustified in their fears. [0]
Vaccine manufactures cannot be held liable.
Thus there is a "National Vaccine Injury Compensation Program" put in place to compensate those that have been damaged by vaccinations.
To date, over $4 billion dollars has been paid out in damages. [1]
Just as mentioned in this article, side effects are major deterrents of any medication. And significant efforts need to be made in order to ensure that side effects do not occlude positives effects.
[0]: https://www.supremecourt.gov/opinions/10pdf/09-152.pdf
[1]: https://www.hrsa.gov/sites/default/files/hrsa/vaccine-compen...