English is not my first language, so I am not entirely certain how to put this into words, but there just isn't any reasoning behind it. Like the video you showed, spoke about the negativity bias. Saying that when something bad happens (autism), they will automatically wonder how this happened and look for some kind of connection. There are more ridiculous theories behind the cause of autism, such as blaming the amount of carbondioxide in the air, the growth of the meat industry and just anything that they believe is harmful. Some people started to point at the vaccines and thanks to the confirmation bias that the video mentioned more followed.
That aside, knowing the cause doesn't mean the same as knowing the solution, since the whole cause is just idiocy and ignorance. We tried the cold hard facts, but they won't help thanks to ignorance.
Now, what do we do with sheep? We shepherd them.
Same with idiots.
Maybe putting this under another light might help get across what Kaga is saying.
Let's look at something such as Religion.
More Specifically the fundamentalist Christians when dealing with:
a) Pushed laws to separate church and state
b) Individuals such as Richard Dawkins or Christopher Hitchens
c) Gay people having the right to marry.
You'll get the occasional one to come out, listen to the arguments being shown and change their religious views as a result.
However, most of those cases have other elements above that either caused them to already be questioning, or simply have weak faith to begin with.
While the Majority of the Fundamentalists have gotten more stubborn, declaring stuff like there is a "War on God!" and then cry that they're being persecuted as a result.
Now translate this back to Vaccines, subsitute "War on God" with "Cover-up Conspiracy" and it's basically the same idea.
They had a certain belief, others showed them facts saying otherwise, they respond to this as if they're being attacked/denied.
Part of the problem here being once someone identifies strongly enough with a belief, they take any attacks or criticisms of said belief personally.
So when people simply barge in and say "Vaccine's don't Cause Autism!" they are going to be instantly defensive and think of any defense they can, even if completely non-nonsensical.
What approach would work better is easing them in, have them open and willing to at least hear the other side out.
And when the other side speaks, do so as if it's among two intelligent individuals. Not one person talking down to another.
Like once again putting it under the other light.
How many times is someone converted to a Religion by being bashed over the head with a Bible being told their evil?
How many times does someone become an atheist after being exposed to enough friendliness and kindness from other Atheist?