The CDC never really said that "masks don't work for public" [0]. Some other health officials and media did. Now, if you relied on the CDC for information everything would be more or less fine. The two things that make this situation worse is - (1) An ever-changing landscape of information and (2) "Whom to listen to?" problem. We are not good at (1) itself, because we are terrible at updating our priors. Then, you throw in (2) in the mix and there's mass confusion.
Zeynep Tufkeci can say that "oh tell the truth" but there's no guarantee that her version of communication would play better than what we have.