What we're striving for is to consume media sources that produce the least number of mistakes when we're reading them - the number of past mistakes may be an indicator on the likelihood of future mistakes or it may not. I think trying to make any strong statements leaning on historical data should be carefully weighed.
I can't really answer what the best tactic for weighing news sources is since I think that the true measure would need to involve observing the reporters and editors behind each specific article which isn't really feasible. I don't think it's wrong for you to be hesitant about trusting NYT, and feel free to never trust an article written by Miller - I personally think she's shown a lack of care for discovering the truth - but... Eh, balance in all things.
But shouldn't we not continue to consume sources that have made malicious mistakes? Even if the maliciousness was a bad outside actor feeding incorrect information to ethical reporters, isn't it likely that such a source will make a malicious mistake again? When the consequences are on the scale of directing the country into a fraudulent war, how can we ever trust their reporting on anything of consequence again?