As far as I can tell Biden and Harris said they distrusted the Trump rollout of the vaccine but not the vaccine itself. https://www.politifact.com/factchecks/2021/jul/23/tiktok-pos...
The factcheck word twisting is getting out of control.
But if anything, this distinction is worse, because instead of saying don't trust a controversial product, it's saying don't trust this controversial product because you shouldn't trust the/this government promoting it.
And that's largely what made this, or magnified it, as a political issue: the broader acceptance of saying it's ok to distrust the government depending on what politician is speaking.
They were responding to being asked if they would take a vaccine developed/released under the Trump administration.
Not: "What's wrong with how this administrator is handling the vaccine?"
Or, "Do you have a problem with how it's going to distributed?" Which didn't significantly change from one administration to the next, and is an impressive logistical feat in it's own right.
Even if, the same logic stands. Sowing distrust in distribution -or any other aspect- is either implicit distrust in the product or distrust in the government pushing it.
What good is expressing distrust in any part of it, except to discourage people from trusting the quality/safety/efficacy of the product itself?
Not "Do you trust that Trump will deliver in time?"
Or anything about reliability being affected by "rushing" things, because when it did arrive in the timeframe Trump promised, no one was concerned about the speediness compromising any quality or reliability.
The election was over by that point.