That's a straw man. Nobody in authority said this once the vaccine was out and it was obvious that immunity wasn't 100% or permanent. All vaccines are different. No one knew until it came out what category this vaccine would fall into. You can still get measles after getting the measles vaccine. But you're much much less likely to die from it.
What the vaccine did do is greatly reduce the severity of the disease, which saved countless lives. See Wuhan, Northern Italy or NYC before lockdown. If the vaccine didn't work, as soon as lockdown ended, the hospitals would have filled to over capacity like they were in those places in the early days.
But I note that the "a politician was wrong once, therefore vaccines can't be trusted" folks don't tend to extend that theory to things like "tax cuts cause economic booms" or "abstinence only sex ed is super effective" sort of statements that have repeatedly flopped in tests.
https://nationalpost.com/news/world/backlash-and-reversal-af...
Yeah okay she spoke out of turn very early after the vaccine was out for a short time. The CDC sucked a lot through this, especially when they refused to recommend masks. But you notice pretty much all of her own underlings are immediately refuting her. To cling to "They told us you wouldn't get covid" when 99% of the people in authority were not saying that, and the few who might have said it were quickly corrected, is disingenuous imo.
The CDC kind of sucks to be honest, and it sure isn't better with the current leadership. But it doesn't mean they're wrong on everything. And the CDC's suckiness is a flimsy excuse to just believe anyone on youtube, regardless of scientific evidence.