Various people gave their hopefully somewhat informed opinion at the time to different members of the media, who reported on it with different levels of accuracy, attributing often undue levels of confidence to it. And that quickly mutated into "the media's trusted sources can confirm that the experts definitely know the vaccine will have exactly these effects and will be effective for these specific cases"
I think it's worth questioning what influence there was in which narratives did or didn't get pushed, but I also think it's worth keeping in mind that the media is also just... fallible.