I think you miss the point entirely. The broader public's perception of the drug is instrumental to its adoption. If the public are led to believe that the medicine is unsafe, the result will be a reduced level of herd immunity as fewer people will take the vaccine.

Medical institutions (CDC, BMJ, Public Health England), the Government, and the broader media (newspapers, TV stations, companies like Facebook) are responsible for encouraging safe and efficacious use of medicine for the good of society, but they can't do that when the narrative is co-opted by anti-vaxxers, the right, and other shameless opportunists.