Television people dream of such “Oh my God” moments. In the final episode of The Jinx, a documentary series which has enthralled America for the last six weeks, Robert Durst, estranged scion of a wealthy real estate family and a suspect in three murder cases, was presented with handwritten evidence strongly linking him to the murder of his close friend Susan Berman in 2000.

Durst remained outwardly unmoved but moments later headed to the lavatory where, apparently unaware he was still wearing a microphone, he muttered: “There it is. You’re caught,” before adding, “What the hell did I do? Killed them all, of course.”

The day before the episode aired Durst, 71, was arrested in New Orleans and has subsequently been charged by Los Angeles prosecutors with Berman’s murder. Case closed and time to raise a glass to the TV series that managed something the police did not: an admission of guilt from a man who has consistently evaded justice.

But the past week has been full of reports of inaccuracies in The Jinx, of timelines messed with and information withheld. As Durst’s story moves beyond the documentary series and into wider public consciousness, questions are being raised about the growing popularity of serialised true crime stories and our feverish response to them.

For true crime is having something of a moment – from the podcast Serial, a word-of-mouth hit last year, to veteran film-maker Nick Broomfield’s Tales of The Grim Sleeper, which taps into post-Ferguson anger at how black stories are ignored to report on a serial killer in South-Central Los Angeles who went undetected for decades, partly because LA police had no interest in attempting to solve the deaths of black women.

Both Tales of the Grim Sleeper and The Jinx are about to air on Sky Atlantic, and Celia Taylor, Sky’s head of unscripted content, says the appeal lies partly in the demands they make of their audience: “These are the sorts of programmes that ask, where do you stand? How do you feel? It’s not just that the stories are brilliant, but that they involve the audience in their tale.”

Small wonder that when people talk of listening to Serial and watching The Jinx, it’s in almost gluttonous terms. They are something to be gulped down, gorged on, binged on, devoured. “Certainly for me, part of the pleasure of watching The Jinx was talking on Twitter afterwards,” says award-winning crime writer Megan Abbott. “It’s a unique feeding frenzy in which every moment has an immediate response.”

Neither does the obsession stop once the series ends. Over its 10-week run, Serial became a global addiction, with fans frantically waiting for each episode before debating online. Four months after the show ended, an impassioned section of Reddit continues to sift through the evidence, positing endless theories as to who really killed Hae Min Lee in 1999. Her former boyfriend, Adnan Syed, the man convicted of the crime, has an appeal hearing scheduled in June.

“The internet draws those who like to go down the rabbit hole,” says Abbott. “You dig your way into people’s lives without having to leave your home. You can sit there uncovering timelines and digging down further and further. It taps into the inner obsessive inside so many of us.”

It’s also an increasingly respectable hobby. Where admitting to enjoying true crime books with their lurid covers and pulpy titles – Helter Skelter, The Stranger Beside Me, Blood and Money – used to draw disapproving sniffs and talk of exploitation, today everyone’s a fan.

“All my life people wanted me to apologise for liking true crime, but Serial came along and made it appropriate,” says Abbott, who has frequently spun her acclaimed novels from real-life events. “New true crime fans love the genre for the same reasons I do – because you go to dark places, because of that slight queasiness – but because Serial is on public radio from the people behind This American Life it’s somehow presented as classier. Peel back the layers and the issues remain the same.”

Chief among those issues is what happens when the thrill of being caught up in a story makes you forget it is someone’s reality. Hae Min Lee died. Susan Berman died. Durst’s neighbour Morris Black died. Kathie Durst, his first wife, whose body has never been found, almost certainly died. Yet both Serial and The Jinx are frequently so enmeshed in the guilt or otherwise of their protagonist that the victim is forgotten.

“It’s that Janet Malcolm thing of how much distance exists between reporter and subject,” says editor and critic Sarah Weinman, referring to Malcolm’s celebrated book The Journalist and The Murderer, which unpicked the complex relationship between journalist Joe McGinniss and convicted killer Jeffrey R MacDonald.

“Malcolm compares the relationship to that between a psychoanalyst and patient, and I think that when you interview anyone at length, as both Andrew Jarecki [director of The Jinx] and Sarah Koenig [presenter of Serial] did, then issues of distance arise.”

That blurring between subject and interrogator has been a component of true crime since Truman Capote claimed to have created the first non-fiction novel with In Cold Blood. His masterfully written tale of the murder of the Clutter family in Holcomb, Kansas, in 1959 was published 50 years ago and remains for many the genre’s benchmark. Yet in his 1988 Capote biography, Gerald Clarke claimed that the final scene, in which detective Alvin Dewey meets the friend of one of the Clutter daughters, was fabricated, while last year a judge ruled that the secret files of one of the FBI agents, which apparently contradict swaths of Capote’s book, could be published for the first time. A book by the agent’s son is expected this year.

Any true crime story is shaped by what is included – or, more pertinently, left out. Rabia Chaudry, Adnan Syed’s childhood friend who initially contacted Koenig about the case, was outspoken in her criticism of aspects of Serial’s reporting, explaining in a talk at Stanford law school that “Sarah’s telling a story, but I want to tell Adnan’s story,” adding that she was frustrated by Koenig’s refusal to push harder at certain witnesses.

“We want true crime narratives to be like mystery novels, to see order created out of chaos,” says Weinman. “The trouble is that in real life the narrative is always messy. Something will always come up we can’t shoehorn into the accepted story no matter how hard we try.”

In The Jinx, that something was the timing of the two interviews with Durst that form the backbone of the series. A New York Times report suggested the timeline surrounding these interviews was murky, raising questions of when exactly Jarecki and co-producer Marc Smerling went to the police. In response, they released a statement: “Given we are likely to be called as witnesses in any case law enforcement may decided to bring against Robert Durst, it is not appropriate for us to comment further on these pending matters. We can confirm that evidence (including the envelope and washroom recording) was turned over to authorities months ago.”

“The thing to remember with The Jinx is that they’re telling a story,” says Weinman. “They needed an ending and found one, but serious questions are raised about why they felt the need to manipulate the timeline and what was left out. I can’t help but feel that now the actual case is back in the spotlight the documentary itself will fade a little or feel less relevant.”

For Taylor, however, the show can withstand the scrutiny: “It was instantly clear this was no ordinary televisionseries. They take a complicated story and tell it incredibly well, and that’s what people respond to, because they need to see how it unfolds.” And for all the controversy, Durst, so long able to evade his interrogators, is behind bars with a murder trial possibly to come. The true crime genre, too, continues to flourish. Veteran documentary maker Errol Morris, whose The Thin Blue Line remains one of the classics of the genre, recently announced that he was working on a six-part series for Netflix, subject matter as yet unknown.

“I wonder if we’ll look back in a few years and say why was this genre so popular at this time, what societal chasm was being filled?” says Abbott. “There’s something about the community aspect of these stories that’s just so strong. In that sense it’s closer to the serialised crime stories of the 19th century, where everyone would buy each issue, then dissect the news. It’s a feeling that’s both new and as old as the hills.”

Tales of the Grim Sleeper and The Jinx will be shown on Sky Atlantic on 30 March and 16 April respectively

FIVE OF THE BEST TRUE CRIME FILMS

Paradise Lost Trilogy Joe Berlinger and Bruce Sinofsky’s films covered the US Robin Hood Hills murders, in which three heavy metal fans were accused of killing three boys in a Satanic ritual. They were released in 2011 after 18 years in jail.

The Staircase This 2004 mini-series by Jean-Xavier de Lestrade follows the case of Michael Peterson, who was convicted of murdering his second wife in 2003.

The Thin Blue Line This 1988 film by Errol Morris argues drifter Randall Adams was wrongly convicted of murdering a Texan policeman. Adams was later released.

Aileen Wuornos: The Selling of a Serial Killer Nick Broomfield’s 1992 film about the murderer, executed in 2002.

The Central Park Five Ken and Sarah Burns’s study of the 1989 arrest of five black teenagers suspected of raping a white woman in Central Park. Another man later confessed to the crime.

• This article was amended on Sunday 22 March 2015 to change the main picture.