“The majority of events thought to be related to the administration of a vaccine are actually not due to the vaccine itself - many are simply coincidental events, others (particularly in developing countries) are due to human, or programme, error.”
EDIT: but, to be fair, it also says: “There is no such thing as a "perfect" vaccine which protects everyone who receives it AND is entirely safe for everyone.”
I just have a hard time believing that those infrequent side effects are worse than the lives saved