Marsha and Carl Mueller of Prescott, Arizona, said the group refused to speak with them for months and then withheld critical information provided by freed Doctors Without Borders hostages -- information that directly concerned their daughter and was needed in order to begin negotiations for her release.
In a phone conversation recorded by the Muellers 10 months after their daughter's kidnapping and provided to ABC News, they asked the group if it would help negotiate for their daughter. "No," the senior official replied. "So, the crisis management team that we have installed for our five people and that managed the case for our people will be closed down in the next week. Yeah? ... Because our case is closed."
"They're a fabulous organization, and they do wonderful work," Carl Mueller told ABC News' "20/20" in an interview to be broadcast this Friday, "but somewhere in a boardroom, they decided to leave our daughter there to be tortured and raped and ultimately murdered."
FULL BRIAN ROSS REPORT: "The Girl Left Behind."
Mueller was killed in ISIS captivity in February 2015, 18 months after she was taken. She was kidnapped as she accompanied her boyfriend, Omar Alkhani, to Syria to help install communications equipment for Doctors Without Borders, also known by its abbreviation in French, MSF.
The organization's top U.S. official said the group had no obligation to help the young American woman because she was not their employee.
"I don't think there was a moral responsibility," Jason Cone, MSF's U.S. executive director, said in an interview with ABC News. "We can't be in the position of negotiating for people who don't work for us."
Cone said Mueller had not been asked by the group to come to Syria and would have not have permitted her to travel there if it had been asked because of her American citizenship.
At least seven staff members of Doctors Without Borders were released by ISIS after the group helped to negotiate ransom payments. But the group refused to include Mueller in the negotiations, or to speak with the FBI case agent handler her case, according to an April 2014 email from a senior Doctors Without Borders official in Brussels provided to ABC News by the family.
Chris Voss, a retired FBI chief hostage negotiator who once oversaw hostage recovery operations in Iraq, said he found MSF's decision not to aid Kayla Mueller or her family "stunning."
"I think that's totally abandoning someone that you had no reason to abandon. I mean, it sets that person up for incredibly negative, horrific consequences," he told "20/20." "They could've said, 'Yes, you work for us.' And they could've extended her some sort of protection, some sort of legitimacy that would've cost them nothing. And why they leave her out there like that? It's frightening. It scares me."
"It's a lack of appreciation for another human being," Voss added.
“If we start engaging in negotiating for the release of non-staff members, we increase the risk to our teams that are already taking grave risks to provide medical care in the some of these same places that Kayla wanted to provide help to,” the Doctors Without Borders executive said.
A Doctors Without Borders press release at the time of Mueller's reported death on Feb. 6, 2015, stated, "Despite media reports, MSF wishes to clarify that at no time was Ms. Mueller employed by MSF, either in Syria or anywhere else."
The group recently deleted the statement from its website, at the request of the Muellers, because "it was insensitive at a time of incredible grief for them," Cone told ABC News.
The young American's horror began on Aug. 3, 2013, with what seemed to be a safe trip from Antakya, Turkey, to Aleppo, Syria, to help Alkhani, who had been hired as a contractor by the group to install a satellite internet device at a hospital run by the group’s Spanish affiliate, according to her family, friends and the FBI. It was late in the day, so the hospital advised they stay overnight. The next day, Aug. 4, Kayla and Omar finished the work and hospital staff put them in an MSF-marked, "locally hired" vehicle to be transported to the Aleppo bus station to return across the Turkish border.
But they never made it.
A large group of ISIS gunmen stopped the vehicle and took prisoner Kayla, Omar, the hospital's assistant logistics manager and the driver. All were Syrian except Kayla and all were released within weeks -- except the young American.
When three female staff members were finally released by ISIS, they had been told to memorize an ISIS email address to give to Kayla’s parents -- but Doctors Without Borders officials failed to tell the Muellers about that for at least seven weeks, until the final two members of its staff were also set free by ISIS.
“We had to take a decision in terms of passing the information on that was in the best interest of the two men that were held,” Cone said.
The delay in handing over the email address probably angered ISIS, said Voss, the former FBI hostage negotiator who once oversaw hostage recovery operations in Iraq.
"Looking at the situation from the adversary's point of view, the Daesh kidnappers, they can't imagine this would happen. This makes no sense to them. They have to be frustrated by this. They have to be kind of confused by it," he said, using an alternative name for ISIS.
ABC News' Rhonda Schwartz, Lee Ferran, Matt McGarry, Engin Bass, Mark Dorian, Alex Hosenball and Cho Park contributed to this report.