Yes, I know that you have a history of accusing people of lying randomly if they upset you.
No organization is 100% accurate, as that is not humanly possible. But the MSM has extremely high standards for accuracy and has evolved a set of practices that are extremely well-crafted to advance the goal of accuracy. As was pointed out in another piece that you refused to read, one of the big challenges is that precisely because the MSM is so credible, bad actors try to lie to them to launder their own false claims. But even there, they have practices that reduce the success of that strategy. Where C&H go is not to accuracy or honesty (separate goals, of course, as one can be honest but not accurate) but to perspective. The idea is that the structures in place in newsgathering work to prevent a sort of deeper analysis of the system. For example, it's taken for granted that U.S. interests should be primary when it comes to foreign policy.
To be clear, there are a lot of stupid CTers on the left, too. And, yes, one cannot hope to advance a reasonable discussion with CTers because they do not look at the world in a reasonable way, and CTism itself acts as a kind of defense against reason.
Are you aware of any organization that more reliably reports facts than the two papers you listed? Maybe the LA Times? Further, as I noted earlier, it's not inaccuracy but accuracy when it contradicts bias that causes mistrust. A hypothetical paper that never made a mistake and gave all issues weight in proportion to their importance would be hated by both the nutter left (people like Dore, Ball, West, etc.) and most of the right.