It may not be proof but you cannot disprove it. What that says is you are willing to gamble a child's life. I am not. No child should be subject to the vaccine when there is claim that death occurred due to the vaccine.
In the 18th and 19th centuries, many children died precisely because their parents objected to vaccination. Unfortunately, anti-vaxxers are nothing new.
There was an interesting show on PBS tonight, called Extra Life: A Short History of Living Longer. The first episode was about vaccines.
It'll probably be rerun later this week. I suggest you check it out.