Honest
What is the definition of safe, is driving a car safe? is going to sleep considered safe?
Is drinking water safe?
Nothing is without risk, yet there is a certain level of risk that is considered to be totally safe.
So no, not everyone agrees that vaccines can cause serious disease more than anything else that we consider safe.
You also mention the federal law with regards to the inserts, while I am not familiar with such a law, why would you think that the inserts would contain potential side effects that are not associated with the vaccine at hand?