With their endless front-page stories about Hillary's emails, only to bury the exoneration on page 16...
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The exoneration happened (and was widely reported) long ago. As I said elsewhere, this new story was, in a sense, "new report confirms previous report" or "Hillary cleared yet again for something she was already cleared for." So to play a little devil's advocate here, how newsworthy is that, really? Should it really be front page news? (Honestly, the people who believe she was already cleared won't see this as important news, and the ones who don't believe she was cleared STILL aren't going to be convinced.)
With the NYT hiring biased right-wing mouthpieces because it values political balance higher than the truth...
NYT has had left and right on the op-ed pages forever. News is supposed to be about truth, op-ed is supposed to be about opinion, and political balance is an acceptable goal in that context.
With the NYT running a sensationalist article on something that never happened...
I guess you're talking about the article that is the subject of the OP... it didn't not happen, but ambiguity in the statement led to a questionable interpretation, and the story here is that they corrected it. Newspapers make mistakes all the time. That's one reason news is the "first draft" of history. Deadline pressures and putting out stories before all facts are known come with the territory.
Seriously, where does this rumor come from that the NYT is somehow more trustworthy than other newspapers?
It's very far from perfect, but there aren't too many that are better.