But in the US, once a case is over, any juror can choose whether or not to speak publicly about a case and their deliberations. Jurors often choose to speak out - some even write books - after high-profile cases like that of Clancy.
The BBC, which was in the court during the case, has confirmed the three women who spoke with NBC were on the jury panel.
In the NBC interview, which aired on Tuesday, the jury foreperson - a retired fifth-grade teacher - called not being able to reach a verdict in the case "awful" and an "emotional roller coaster". A foreperson acts as a spokesperson for a jury in any US legal case, meaning they are the person delivering a verdict and sending notes to the judge on behalf of the 12-person panel.
She said the deliberations were difficult and filled with "lots of crying" and "lots of tears and then hugging".
"I was so sad, so sad that we couldn't come up with a verdict for Lindsay. It was so heartbreaking," she added.
Throughout the interview, the three women said the jury was in nearly unanimous agreement to enter their verdict but the holdout juror would not change his mind.
The foreperson said the lone juror "admitted he had reasonable doubt and I started filling out the forms, I was so excited".
She was halfway through filling out the verdict sheets when the holdout juror, who she said was a man, continued: "But I'm still not going to say that she's not guilty by reason of insanity," she says he told the panel.
The man in question has not come forward and has not responded to these comments.
The three jurors noted their deliberations led to fights and yelling, which at times could be heard through the walls.
Under Massachusetts law, there was no burden on Clancy to prove her mental illness and that she lacked criminal responsibility. Rather, it was on the prosecution to prove beyond reasonable doubt she was criminally responsible when she killed her children, criminal defence lawyer Elyse Hershon previously told the BBC.
"We weren't trying to figure out if she murdered the children. She did and she's admitted that," the foreperson explained in the interview with NBC. "We're trying to figure out - did she know right from wrong at that time. "
The three jurors noted they didn't feel persuaded by the prosecution.
"Everything proved that she loved her children so she had to have snapped and not known what she was doing," the foreperson said.
Another juror, who does work for a government defence contractor, said the holdout juror had questions about what medication Clancy was on.
"We had the toxicology reports. We could see exactly the amounts," she said, adding that there were nurses on the jury who spoke about that. "He just completely disregarded the information that they gave," the juror added.
The third juror, a chef at a senior centre, said she found the prosecutors in the case to be "very, very harsh", adding: "They had no character witness in regard to Lindsay of being a bad mother. "
The grim case led to a series of dramatic twists and turns as the jury deliberated for nearly 40 hours over seven days to determine Clancy's fate. They signalled multiple times they were facing a deadlock - and at one point told the judge that one member of the panel was not following the judge's instructions on reasonable doubt.
The development led to Clancy's defence attorney requesting the holdout juror be removed from the panel - a request that was quickly denied - before the panel again said they could not come to a unanimous decision.
Judge William Sullivan then declared a mistrial on Friday.
The mistrial leaves both the case and Clancy's future uncertain, as prosecutors determine whether they want to take the case to trial a second time with a new jury.
Clancy's lawyer, Kevin Reddington, has since said he so the case doesn't see a second trial.
The three jurors told NBC they hoped there wasn't a second trial - but if there is - all three said they plan to attend in support of Clancy.