No, that's not what people are doing. For many years science reported time and time again of the link between mercury preservatives and autism. People with disabled children are desperate to understand why their child is affected and the link, from authoritative sources, seems to make sense. Science created this problem with the false reports, published in respected journals, and supported by numerous other studies over the years. Then suddenly the original reports are discredited as the work of a liar and a cheat and all of the people that read those reports over time are supposed to change their minds? No way.
I've discussed this with university educators as recently as four years ago that were fully convinced of the relationship between autism and vaccination and who marked my daughter's reports down when her writing questioned that link.
It's going to take years to undo the harm done by the original and follow up reports. Public perceptions of risks and benefits are not objective. And right now there is little epidemic consequence to not having vaccinations. But when enough people are no longer covered, and kids start dying from polio, whooping cough, and other formerly controlled problems, the fault is all going to rest with those that wrote and published the lies about the relationship.