First of all, does the Clinton campaign really need to start talking about "conspiracy theories" for the NYT to notice what in the 1990s was called "the politics of personal destruction"? In a word, no.
For example, Bad Pols or Bad Polls was the question we posed June 20 with a follow-up on July 2 on the NYT Upshot response of Exit Polls, and Why The Primary Was Not Stolen From Bernie Sanders. In the Upshot piece, Nate Cohn swatted away the conspiracy theories of a -you guessed it - rigged election. Between June 20 and July 2 the NYT had ignored that conspiracy theory, presumably as unworthy of reporting, until the conspiracy theories became too widespread to ignore.
From what I hear, there is a tense relationship between the NYT news folks and the Upshot.
Still, why does the NYT News department need to report every story that relates to politics as a "he said/she said story" in this instance waiting for a Clinton campaign response before reporting conspiracy theories? Well, because to meet the NYT standard of journalistic integrity, you must be objective, and to be objective you must report what one side does, then go to the other side for their reaction, then go back to the other side, and so on. Every person is a potential voter and if you vote you are therefore biased and nonobjective and therefore ineligible to make intelligent interpretations of the evidence. So the story goes - there is an Opinion section for opinion. Sorry, but that system fails. Waiting for the Clinton campaign's reaction dignifies all allegations against the candidate and misses the meta-story - the fact of an intense campaign of never-ending allegations of wrongdoing that persists until one of the allegations can stick and then working that allegation to death.
While the NYT has begun to question their definition of objectivity, notably on the Business/Media page, it should not have been necessary to have the extreme case of candidate Trump for this process of questioning to begin.
Back to that Media article - it begins,
If you’re a working journalist and you believe that Donald Trump is a demagogue playing to the nation’s worst racist and nationalistic tendencies, that he cozies up to anti-American dictators and that he would be dangerous with control of the United States nuclear codes, how the heck are you supposed to cover him?
That misidentifies the problem. The problem for a journalist is not having beliefs about the person. The problem is that when a candidate makes an important statement that is false, the journalist need not necessarily go to the opponent to seek the response. Just say the statement is false and important if it is. Say why it is important. If not important, say so. Otherwise readers are left with a back and forth between candidates and a general sense of balance which is responsible for the false equivalency that is intrinsic to political reporting in NYT and a little less so in Wapo. And if attacks by a candidate or supporters are unconscionable, as the relentless personal attacks on Clinton staffer Huma Abedin, certainly appear to be, as a matter of principle, then say so - or at least report that there is a context of continual personal attacks.
We are often told we live in a polarized time, but that so-called polarization is largely a result of failure by the objective media to do their job - not a problem of giving Trump too much air time, but failing to call it like they see em. Imagine an umpire calling balls and strikes, not objectively based on what he sees, but by asking the batter and the catcher whether it was a ball or a strike and if they disagree, then asking - "he says it was low and inside", "No, it was right down the pipe." Let's check with the manager.