“Crazypants bullshit” is not a phrase one might expect to hear in America’s most prestigious newsroom, but the Trump administration has rewritten all of the rules of journalism. The chiefest challenge facing paper of record the New York Times upon the current commander-in-chief’s election was not facing down a political operator who made enmity for news media a pillar of his campaign platform; the real task was to adapt and evolve, forging a new methodology of reportage for a time in which nothing could be taken for granted. Starting in January 2017, there were no more slow news days at the Grey Lady.

As its closing selection, the Tribeca film festival screened the 90-minute first installment of documentarian Liz Garbus’s three-part series chronicling the Times’s handling of Trump’s calamitous first year in office. And oh, what a year it was: the first segment tackles approximately the first hundred days following inauguration, concluding with an ominous closeup of the word “collusion”, and that period alone brought what would have otherwise been a presidential term’s worth of scandal. The audience gets an intimate peek at the major players as they assemble their coverage of possible partisanship in the FBI’s intelligence gathering operations, an unsavory link to Russian officials, the White House’s selective barring of press from official briefings, and the first handful of resignations, to name only a few. It is all engaging in the specific way a good procedural ought to be, making the process of learning about the nitty-gritty as tense and kinetic as a car crash.

Garbus gets a level of access that only comes with a long, esteemed career and a few Oscar nominations. She moves freely through the Times’s bureaus in both New York and in Washington, often capturing both sides of a key conference call. The best footage comes from this omnipresence that opens private moments up to the general public; she follows some key reporters home to get an impression of personal lives constantly disrupted by a news cycle that refuses to yield. There’s a brief spike of real sadness as Trump expert Maggie Haberman reassures her children that you can’t die inside a dream while she hustles to catch a cab at Union Station. In the first installment’s most charged moment, the camera stays with the Washington team as they watch the New York desk rewrite a lede and change its overall meaning right before their eyes. Unfazed by the camera hovering around her, bureau chief Elisabeth Bumiller curses out the New York shot-callers and threatens to quit.

These two moments convey a raw, unfiltered perspective even as they respectively illustrate Garbus’s major oversights. Regarding Haberman in specific – Garbus joins her in a car as she takes the flak from a tweet describing Trump as “collected”, with many social media users disappointed with what they perceive as unduly soft treatment. Haberman sighs, says she’s tired, and Garbus moves right along without once considering that one of the sculptors of Trump’s public profile may be setting the bar low. That moment speaks to a larger hesitance to criticize an institution that’s vital, but far from perfect. The disconnect between the Hill and the Big Apple glances past the insight that the Times is a large, often fractious organization with an op-ed page constantly, brashly contradicting its news section. During a Q&A following the Tribeca premiere, the Times’s executive editor, Dean Baquet, confirmed that following episodes would remain focused on the newsroom, and not address the decision to give a weekly platform to the likes of David Brooks.

But the noble intentions of Garbus’s project predispose a viewer to cut her a bit of slack on these cop-outs. These are dire times, as one newswriter writes and then deletes in favor of the more innocuous “bizarre”, and maintaining a house of truth such as the Times’s towering midtown headquarters should be a national concern. An apocalyptic score from Atticus Ross and Trent Reznor really drives home the “dear lord, the world is coming to an end” atmosphere, even when juxtaposed somewhat comically with the banality of typing and clicking. Garbus looks to the Times and their stalwart rivals at the Washington Post as the final line of defense against an onslaught of crazypants bullshit, and her subjects know better than to buy into their own hero-myths. This real-life Spotlight sans Hollywood histrionics comes not a moment too soon, though this critic has doubts about the series’ efficacy in winning over the tinfoil-hatted set convinced NBC’s out to get them. If facts are the Trumpista’s mortal enemy, what use could they have for a meticulously produced “How It’s Made” episode about information?

• The Fourth Estate was showing at the Tribeca film Festival and will start on Showtime on 27 May with a UK date yet to be announced