The same standard could be used to trivially censor literally any information from any outlet. Conservatives could censor all NYTimes articles because they have compelling evidence the NYTimes newsroom is taking money from foreign sources (they are), has a history of releasing false information (they do, all news outlets eventually do), and being biased against conservatives.
In fact, your standard would censor precisely the MOST important stories, because these are the most likely to influence elections.