For context, that was in June 2021, in August 2021 he said this:

> Let me be clear: There are cases where vaccinated people do get COVID-19, but they are far less common than unvaccinated people getting COVID-19. And most importantly, their conditions are far less severe.

https://www.whitehouse.gov/briefing-room/speeches-remarks/20...

So the "government propaganda" is... unprepared statements by individuals being live-interviewed, which were so unusual and against accepted-truth that they provoked immediate and public correction from mainstream news outlets, as well as corrections (or at least distancing) by the rest of the government?

Even a brief look at the context shows those are "exceptions that prove the rule."

I'm sure that for some people those incidents defined "what [they knew] the government said", but that would probably be because they put themselves into media-bubbles which excluded the greater mass of nuanced (and boring) health information, allowing only the "OMG look at this" scornful submissions by their Facebook friends.

> So the "government propaganda" is... unprepared statements by individuals

Yes, when those individuals are the president of the US and the director of the CDC presenting half-truths and exaggerations to further their agenda, that is textbook government propaganda.