Vaccination are meant to prevent things, not to cause them. In case of the isolated tragedies, it is very hard to determine what was the real cause and why that child in particular.
Like you said, even with all the science in the play, doctors failed to diagnose a simple thing.
The specialists should be hand picked and not placed in the hospitals based whose parent is what, sadly we sometimes end up with the army of incapable idiots incapable curing a simple cold....