The problem is the government and traditional media have been caught lying again and again. Once that trust is broken I don't know how you rebuild it. Hell people I commonly talk to still believe a police officer was beaten to death on 1/6 and that people, other then the women shot for trying to enter the chambers, died directly due to the riot. All because of that what the news reported and quietly fixed days later…
Note that, while I didn't personally consume any sources of news making these mistakes about this event and therefore can't reasonably comment on them, this specific wording is used extremely commonly as an uncharitable attack on those who are opposite to one's own political leanings. I.e. corrections are always described as "quiet" despite frequently being published in the same manner as the original material.