The media stories would have come out either way.
Some people are set to not take a vaccine, they will take whatever version of this story as an argument for their view point. It is not about them.
But take someone like my father (76) as example. Not anti—vaccine at all, but a bit cautious and not in a hurry to get it. If there are stories from reputable news papers, that vaccine A causes X issue but government keeps giving them out, he would not take it. If on the other hand it got stopped, investigated and found to be harmless he would be open again.
If based on the data it should be continued to be given out while investigation is ongoing, I don’t know. I think as with a lot of things about this pandemic and it’s handling in different countries it will maybe take years to have conclusive insights in hindsight what were the right decisions.